Quantitative Aptitude

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Quantitative Aptitude

1)PROFIT & LOSS 1. Arun went to buy an Android mobile, the shopkeeper told him to pay 20% tax if he asked the bill. Arun manages to get the discount of 5% on the actual sale price of the mobile and he paid the shopkeeper Rs. 8550 without tax. Besides he manages to avoid to pay 20% tax on the already discounted price, what is the amount of discount? A.2685 B.2636 C.2250 D.2675 E.2690 Answer & Explanation

Answer – C.2250 Explanation : CP = 100, SP (with tax) =120 New SP = 100 – 5 = 95 Discount = 120 – 95 = 25 Discount = 25/95 * 8550 = 2250 2. Cost Price of two mobiles is same. One is sold at a profit of 20% and the other for Rs. 5200 more than the first. If the net profit is 40%. Find the cost price of each mobile? 2|Page

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A. Rs. 13000 B. Rs. 12000 C. Rs. 16000 D. Rs. 12500 E. None of these Answer & Explanation

Answer – A. Rs. 13000 Explanation: CP of each mobile be Rs.x then (2 x 1.20 x x) + 5200 = 2 x 1.4 x N ⇒ 0.4 x = 5200 ∴ N = 13000

3. Rahul sells his laptop to Ravi at a loss of 20% who subsequently sells it to Suresh at a profit of 25%. Suresh after finding some defect in the laptop, returns it to Ravi but could recover only Rs.4.50 for every Rs. 5 he had paid. Find the amount of Suresh’s loss if Rahul had paid Rs.50,000 for the laptop ? A. Rs.6000 B. Rs.7000 C. Rs.2000 D. Rs.5000 E. None of these 3|Page

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Answer & Explanation

Answer – D. Rs. 5000 Explanation : 0.50/5 * 50,000 = 5000 4. A reduction of 20% in the price of sugar enables a housewife to purchase 6 kg more for Rs. 240. What is original price per kg of sugar? A. Rs.10 per Kg B. Rs.8 per Kg C. Rs.6 per Kg D. Rs.5 per Kg E. None of these Answer & Explanation

Answer – A. Rs.10 per Kg Explanation : Explanation: Reduction in price = 1/5 = 20% Increase in Quantity = 25% 25% = 6 Kg. original amount of Sugar = 6*4 = 24Kg. Original price of the sugar = 240/24 = Rs. 10 per kg. 5. A Bike is available at 40% discount at show room “A” and the same is available at only 25% discount at show room “B”. Mr. Arun has just 4|Page

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Quantitative Aptitude

sufficient amount of Rs. 60,000 to purchase it at show room “A”. What is the amount that Mr. Arun has less than the required amount to purchase it at that show room “B”? A. Rs. 70000 B. Rs. 50000 C. Rs. 10000 D. Rs. 15000 E. None of these Answer & Explanation

Answer – D. Rs. 15000 Explanation : Let the marked price be x. Cost price (CP) = 40 % discount on MP = 0.6y = 60000 ⇒ y= Rs.100000 MP

SP at Show Room “A” = Rs. 60000 SP at Show Room “B” = 100000 X 0.75 = 75000; Difference = 15000 6. Person A sold his car to Person B at a profit of 20% and B sold it to C at a profit of 10%. Person C sold it to mechanic at a loss of 9.09%. Mechanic spent 10% of his purchasing price and then sold it at a profit of 8.33% to Person “A” once again. What is the loss of person “A”? A. 23% 5|Page

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B. 29% C. 50% D. 40% E. None of these Answer & Explanation

Answer – A. 23% Explanation : A: CP = 100 SP = 120 B: CP = 120 SP = 132 C: CP = 132 SP = 120 Mechanic: CP = 120 + 12 = 132 SP = 143 Loss of A = 143 – 120 = 23 % loss of A = (23 / 100) x 100 = 23% 7. A and B are two partners and they have invested Rs. 54,000 and Rs. 90,000 in business. After one year A received Rs 1200 as his share of profit out of total profit of Rs. 4200 including his certain 6|Page

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Quantitative Aptitude

commission on total profit since he is a working partner and rest profit is received by B. What is the commission of A as a percentage of the total profit? A. 1200 B. 1100 C. 1500 D. 1250 E. None of these Answer & Explanation

Answer – A. 1200 Explanation : Explanation: Ratio of profit of A : B (excluding commission of A) = 54000 : 90000 =>3 : 5 Now the share of profit of B = 4200 – 1200 = Rs. 3000 So the share of profit A (excluding commission) = Rs. 1800 So the commission of A = 3000 – 1800 = 1200 8. A shopkeeper bought 150 pen drives at the rate of Rs. 500 per pen drive. He spent Rs. 500 on transportation and packing. If the marked price of pen drive is Rs. 520 per pen drive and the shopkeeper gives a discount of 5% on the marked price then what will be the percentage profit gained by the shopkeeper? 7|Page

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A. 4.5% B. 5.5% C. 3.8% D. 1.2% E. None of these Answer & Explanation

Answer – C. 3.8% Explanation : C.P. of 150 calculators = 150 x 500 = Rs. 75000 ∴ Total C.P. = 75000 + 500 = Rs. 75500

Marked price of 150 calculator = 150 x 570 = Rs. 82500 Selling price after discount = 82500 x 95 / 100 = Rs. 78375 ∴ percentage profit = [(78375 – 75500) / 75500] x 100 = 3.8%

9. A vendor has two types of grapes. One is the fresh grapes containing 80% water and dry grapes containing 25% water. He sells 20 kg dry grapes, by adding water to the dry grapes, at cost price. What is the total profit percentage when after adding water the weight of 20 kg dry grapes increase in the proportion of water in fresh grapes? A. 265% B. 200% C. 280% 8|Page

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D. 275% E. None of these Answer & Explanation

Answer – D. 275% Explanation : Fresh grapes Water: Pulp = 80% : 20% = 4 : 1 Dry grapes Water: Pulp = 25% : 75% = 1 : 3 So out of 20 kg dry grapes, Water : Pulp = 5 kg : 15 kg After adding of water the ratio of water : pulp is same as the fresh grapes = 4 : 1 After adding water the quantity of Water and Pulp are 60 kg and 15 kg respectively. % = 55/20 * 100 = 275% 10. Pinkey and Shalini invested some amount of money in the ratio of 3:5 for the same period in the business. They decided that at the end of the year 20% profit was to be given to an organization as a donation. Out of the remaining, 75% was to be reinvested and the rest of the profit was to be divided as interest on their capitals. If the difference in their share is Rs. 2400. What is the total profit? A. 49800 9|Page

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B. 49400 C. 48000 D. 49500 E. None of these Answer & Explanation

Answer – C. 48000 Explanation : Let the total profit = 100 Amount left after donation = 50 Amount left after reinvestment = 20 Now, 5x/8 – 3x/8 = 2400 ⇒ 2x/8 = 2400 = 9600

⇒ 1/5 of y = 9600 => y = 48000

2.RATIO &PROPOTION

1. An amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.X, and the difference between Q and R’s share is Rs.3000. Find the total amount of money? A.11000 B.12400 C.13200 D.14300 E.None of these 10 | P a g e

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Answer & Explanation

Answer – C.13200 Explanation : 12a-7a = 3000 5a = 3000 a = 600 7a-4a = x 3a = x x = 1800 22*600 = 13200 2. If a certain amount X is divided among A, B, C in such a way that A gets 2/3 of what B gets and B gets 1/3 of what C gets, which of the following is true A.C’s Share = 1053 and X = 1666 B.A’s Share = 238 and X = 1638 C.B’s Share = 234 and X = 1666 D.C’s Share = 1053 and X = 1638 E.A’s Share = 351 and X = 1638 Answer & Explanation

Answer – D.C’s Share = 1053 and X = 1638 Explanation : A= 2/3 B; B= 1/3C; A:B = 2:3 ; B:C = 1:3; 11 | P a g e

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A:B:C = 2:3:9 C = 9/14 * 1638 = 1053 3. Seats for Mathematics, Science and arts in a school are in the ratio 5:7:8. There is a proposal to increase these seats by X%, Y% and Z% respectively. And the ratio of increased seats is 2:3:4, which of the following is true? A.X = 50; Z = 40 B.Y = 40; Z = 50 C.X = 40; Z = 75 D.X = 50; Z = 40 E.Y = 50; X = 75 Answer & Explanation

Answer – C.X = 40; Z = 75 Explanation : Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x) i.e., (140/100 * 5x), (150/100 * 7x) and (175/100 * 8x) i.e., 7x, 21x/2 and 14x Required ratio = 7x:21x/2:14x = 14x : 21x : 28x = 2:3:4 4. An amount of money is to be distributed among P, Q and R in the ratio of 7:4:5 respectively. If the total share of P and R is 4 times the share of Q, what is 12 | P a g e

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Quantitative Aptitude

definitely Q’s share? A.2000 B.4000 C.6000 D.Data inadequate E.None of these Answer & Explanation

Answer – D.Data inadequate Explanation : Total sum not given 5. Two candles of same height are lighted at the same time. The first is consumed in 3 hours and second in 2 hours. Assuming that each candles burns at a constant rate, in how many hours after being lighted, the ratio between the first and second candles becomes 2:1? A.2 hour B.2.5 hour C.4 hour D.4.5 hour E.None of these Answer & Explanation

Answer – D.4.5 hour Explanation : 13 | P a g e

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Quantitative Aptitude

Height of both candles are same i.e. h First one takes 6 hours to burn completely, so in one hour = h/3 Similarly second one will burn in one hour = h/2 Let after t time, ratio between their height is 2:1 so, remaining height of first candle = h – t*(h/3) similarly for second candle = h – t*(h/2) ratio given 2:1, h – t*(h/3) / h – t*(h/2) = 2/1 Solving we get t = 9/2 = 4.5 6. If A and B together have a certain amount X and if 4/15 of A’s amount is equal to 2/5 of B’s amount, which of the following is true? A.A = 1767; X = 2675 B.B = 1070; X = 2895 C.A = 1767; X = 2945 D.B = 1158; X = 2585 E.A = 1605; X = 2945 Answer & Explanation

Answer – C.A = 1767; X = 2945 Explanation : 4/15 * A = 2/5 * B A= 2/3 B; A:B = 3:2; A = 3/5 * 2945 = 1767 14 | P a g e

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Quantitative Aptitude

7. A sum of Rs.4880 was divided among boys and girls in such a way that each boy gets Rs.44.50 and each girl get Rs. 55.25. If the total number of girls and boys is 100, find the number of girls? A.60 B.50 C.40 D.30 E.None of these Answer & Explanation

Answer – C.40 Explanation : x+y=100 ————– (i) 44.50x + 55.25y = 4880 ————– (ii) Solving (i) and (ii) Y = 40 8. The income of Vinay and Prakash are in the ratio of 4:5 and their expenditure is in the ratio of 2:3. If each of them saves 5000, then find their income. A.11000, 8550 B.12000, 7750 C.15000, 8750 D.13000, 9780 E.None of these Answer & Explanation 15 | P a g e

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Answer – C.15000, 8750 Explanation : 4x – 2y = 5000 and 5x – 3y = 5000. X = 8750, so income = 8750 and 15000 9. If the ratio of the first to second is 2:3 and that of the second to the third is 5: 8, then which of the following is true, A.Sum = 98; A = 48 B.Sum = 147; B = 30 C.Sum = 147; C = 45 D.Sum = 98; B = 30 E.Sum = 98; C = 72 Answer & Explanation

Answer – D.Sum = 98; B = 30 Explanation : A:B:C = 10:15:24 If sum = 98, B = 15/49 * 98 = 30 10. A bag contains 25p coins, 50p coins and 1 rupee coins whose values are in the ratio of 8:4:2.If the total values of coins isX and the total amount in rupees is Y,thenwhich of the following is true A.X = 840; Y = 260 B.X = 966; Y = 345 C.X = 840; Y = 280 16 | P a g e

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D.X = 740; Y = 260 E.None of these Answer & Explanation

Answer – C.X = 840; Y = 280 Explanation : Value is given in the ratio 8:4:2. (8x/0.25) + (4x/0.5) + (2x/1) = 840. X = 20. Total amount, Y = 14*20 = 280

3.AVERAGE 1. The average monthly expenditure of Mr.Ravi’s family for the first three months is Rs 2,750, for the next three months is Rs 2,940 and for the last three months Rs 3,150. If his family saves Rs 4980 for nine months, find the average monthly income of the family for the 9 months? A. Rs. 3800 B. Rs. 3500 C. Rs. 3400 D. Rs. 4200 E. Rs. 4500 Answer & Explanation

Answer – B. Rs. 3500 Explanation : 17 | P a g e

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Quantitative Aptitude

Average monthly expenditure for 3 months = Rs. 2750 Total expenditure for 3 months = Rs 2750 x 3 = Rs. 8250 Average monthly expenditure for 3 months = Rs. 2940 Total expenditure for 3 months = Rs 2940 x 3 = Rs. 8820 Average monthly expenditure for 3 months = Rs. 3150 Total expenditure for 3 months = Rs 3150 x 3 = Rs. 9450 Total savings for 9 months = 4980 Average monthly income for 9 months = (8250 + 8820 + 9450 + 4980)/9 = 3500 2. The average age of a family of 8 members is 24 years. If the age of the youngest member be 6 years, the average age of the family at the birth of the youngest member was? A. 23.42 years B. 21.42 years C. 27.42 years D. 26.42 years E. 24.42 years Answer & Explanation

Answer – B. 21.42 years Explanation: Total present age of the family (8*24) = 192 years Total age of the family 6 years ago = (192 – 6*7) = 150 years At that time, Total members in the family = 7 18 | P a g e

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Quantitative Aptitude

Therefore Average age at that time = 150/7 = 21.42 years 3. Mr. Ravi’s family has 10 males and a few females, the average monthly consumption of rice per head is 8 kg. If the average monthly consumption of rice per head be 10 kg in the case of males and 6 kg in the case of females, find the number of females in Ravi’s family? A. 2 B. 4 C. 6 D. 10 E. 8 Answer & Explanation

Answer – D. 10 Explanation: Let number of females be x. (10*10+x*6)/(10+x) = 8 => x = 10 4. In a famous hotel the rooms were numbered from 201 to 230, each room gives an earning of Rs. 5000 for the first fifteen days of a month and for the latter half, Rs. 3000 per room. Find the average income per room per day over the month. 19 | P a g e

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(September)? A. 2000 B. 3000 C. 4000 D. 5000 E. 3500 Answer & Explanation

Answer – C. 4000 Explanation: Total number of rooms = 29 Average = [(5000 * 30 * 15) + (3000 * 30 * 15)]/(30*30) Average earning per room = 4000 5. In a famous hotel, the rooms are numbered from 101 to 130 on the first floor, 201 to 220 on the second floor and 301 to 330 on the third floor. In the month of September, the room occupancy was 50% on the first floor, 80% on the second floor and 40% on the third floor. If it is also known that the room charges are Rs 200, Rs. 250 and Rs. 300 on each of the floors respectively, then find the average income per room in the hotel for the month of September? A. Rs. 123.75 B. Rs. 132.50 20 | P a g e

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C. Rs. 128.50 D. Rs. 143.50 E. Rs. 223.75 Answer & Explanation

Answer – B. Rs. 132.50 Explanation: Total number of rooms in first, second and third floor = 30, 20, 30 Occupied rooms in first, second and third floor = 15, 16, 12 Average income = (15 * 200 + 16 * 250 + 12 * 300)/ 80 = Rs. 132.5 6. There were 46 students in a Boys hostel. Due to the admission of eight new students the expenses of the hostel mess were increased by Rs.42 per day while the average expenditure per head diminished by Rs 1. What was the original expenditure of the hostel mess? A. Rs.562 B. Rs.542 C. Rs.532 D. Rs.452 E. Rs.552 Answer & Explanation 21 | P a g e

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Answer – E. Rs.552 Explanation: 54*(x−1)−46*x = 42 8x = 96 x = 12 Original total expenditure: 46*x = 46*12 = Rs.552 7. The average salary of the entire staff in a office is Rs 250 per month. The average salary of officers is Rs 520 and that of non-officers is Rs. 200. If the number of officers is 15, then find the number of non–officers in the office A.823 B. 81 C. 87 D. 56 E. 62 Answer & Explanation

Answer – B. 81 Explanation: Let the required number of non–officers = x 200x + 520 x 15 = 250 ( 15 + x ) 250x – 200x = 520 * 15 – 250 x 15 50x = 4050 x = 81 22 | P a g e

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8. Mr.Suresh’s average monthly expenditure for the first four months of the year was Rs.260 For the next five months,the average monthly expenditure was Rs.40 more than what it was during the first four months. If he spent Rs.560 in all during the remaining three months of the year, Find what percentage of his annual income of Rs.5000 did he save in the year? A. 42% B. 48% C. 38% D. 24% E. 28% Answer & Explanation

Answer – C. 38% Explanation: Suresh’s average monthly expenditure for the first four months of the year = Rs.260. 260 * 4 = Rs. 1040 For the next five months,the average monthly expenditure was Rs.40 more than what it was during the first four months. He spent 260 + 40 for one month In 5 months he spent 300 * 5 = 1500 He spent Rs.560 in all during the remaining three months of the year. 23 | P a g e

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Total expenditure = 1040 + 1500 + 560 = 3100 Savings = 5000-3100 = 1900 % savings = 1900/5000 * 100 = 38% 9. The average age of a group of persons going for tour to Shimla is 22 years. 25 new persons with an average age of 10 years join the group and their average age becomes 12 years. The number of persons initially going for tour is? A. 10 B. 8 C. 7 D. 5 E. 4 Answer & Explanation

Answer – D. 5 Explanation: Initial number of persons = x = 22x + 25 * 10 – 12(x + 25) = 22x + 250 – 12x – 300 10x = 50 x=5 10. In English exam, the average of Class “A” was found to be “x” marks. After deducting a computational error, the average marks of 100 24 | P a g e

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candidates got reduced from 74 to 54. The average thus came down by 25 marks. The total numbers of candidates who took the English exam were? A. 50 B. 20 C. 80 D. 70 E. 60 Answer & Explanation

Answer – C. 80 Explanation: (74 – 54) * 100 = 25 * x x = 20 * 100 / 25 = 80

4.MIXTURES AND ALLIGATIONS 1. Two vessels A and B contain a mixture of Milk and Water. In the first vessel (i.e) Vessel A has the ratio of Milk to water is 8 : 3 and in the second vessel, Vessel B has the ratio of 5 : 1. A 35 litre capacity vessel is filled from these two vessels so as to contain a mixture of Milk and water in ratio of 4 : 1. Then how many litres should be taken from the first vessel, Vessel “A”. A. 12 L B. 17 L 25 | P a g e

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C. 14 L D. 11 L E. None of the Above Answer & Explanation

Answer – D. 11 L Explanation : [8/11(x) + 5/6(35-x)]/[3/11(x) + 1/6(35-x)] = 4/1 x = 11 2. When one litre of water is added to a mixture of milk and water, the new mixture contains 25% of milk. When one litre of milk is added to the new mixture, then the resulting mixture contains 40% milk. What is the percentage of milk in the original mixture? A. 100/6 % B. 50/6 % C. 100/3 % D. 50/3 % E. None of the Above Answer & Explanation

Answer – C. 100/3 % Explanation : Original Mixture = x L In (x + 1) Mixture, quantity of milk = (x + 1)* (25/100) 26 | P a g e

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= (x + 1)/4 one litre of milk is added to the new mixture [((x + 1)/4 )+ 1 ]/ x + 2 = 40% x = 3 ; quantity of milk = (3 + 1)/4 = 1L percentage of milk in the original mixture = 1/3 * 100 = 100/3 % 3. The price of a box and a pen is Rs.60. The box was sold at a 40% profit and the pen at a loss of 10%. If the Shop keeper gains Rs.4 in the whole transaction, then how much is the cost price of Box? A. Rs.10 B. Rs.30 C. Rs.20 D. Rs.40 E. None of the Above Answer & Explanation

Answer – C. Rs.20 Explanation : 40x/100 – 10(60-x)/100 = 4 40x + 10x = 400 + 600 x = 20 4. A vessel contains a mixture of diesel and petrol in which there is 20% diesel. Five litres are drawn off 27 | P a g e

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and then the vessel is filled with petrol. If the diesel present in the mixture is now 15% then how much does the vessel hold? A. 10 L B. 20 L C. 30 L D. 40 L E. None of the Above Answer & Explanation

Answer – B. 20 L Explanation : 20/15 = x/x-5 x = 20 5. In a lab, two chemical solutions Acid “A” with 90% purity and Acid “B” with 96% purity are mixed resulting in 24 litres of mixture of 92% purity. How much is the quantity of the first solution, Acid “A” in the resulting mixture? A. 12 L B. 20 L C. 16 L D. 14 L E. None of the Above Answer & Explanation 28 | P a g e

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Answer – C. 16 L Explanation : 90x + (24 – x)* 96 = 24 * 92 x = 16 6. 60 kg of a certain variety of Sugar at Rs.32 per kg is mixed with 48 kg of another variety of sugar and the mixture is sold at the average price of Rs.28 per kg. If there be no profit or no loss due to the new selling price, then what is the price of second variety of Sugar? A. Rs.25 B. Rs.23 C. Rs.29 D. Rs.27 E. None of the Above Answer & Explanation

Answer – B. Rs.23 Explanation : Total CP of first variety = 60 * 32 = 1920 Total CP of second variety = 48 * x = 48x SP of Mixture = 1920 + (108 * 28) = 3024 1920 + 48x = 3024 => x = 23 7. Six litre of milk was taken out from a vessel and is then filled with water. This operation is performed 29 | P a g e

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two more times. The ratio of the quantity of milk now left in vessel to that of the water is 8 : 27. How much is the quantity of the milk contained by the vessel originally? A. 18 litre B. 16 litre C. 14 litre D. 12 litre E. None of the Above Answer & Explanation

Answer – A. 18 litre Explanation : [x(1-6/x)/x]³ = (8/27) [x(1-6/x)/x]³ = (2/3)³ (x-6)/x = 2/3 x = 18 8. A vessel is filled with 120 litres of Chemical solution, Acid “A”. Some quantity of Acid “A” was taken out and replaced with 23 litres of Acid “B” in such a way that the resultant ratio of the quantity of Acid “A” to Acid “B” is 4:1. Again 23 litres of the mixture was taken out and replaced with 28 litre of Acid “B”. What is the ratio of the Acid “A” to Acid “B” in the resultant mixture? A. 43 : 29 30 | P a g e

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B. 46 : 23 C. 47 : 21 D. 46 : 29 E. None of the Above Answer & Explanation

Answer – D. 46 : 29 Explanation : In 23 litre mixture, Quantity of Acid “B” = 23 * 1/5 = 4.6 litre Acid “A” in the mixture = 23 – 4.6 = 18.4 litre 120 – x / 23 = 4 / 1 x = 28 Ratio = 92-18.4 : 18.4 + 28 Ratio = 46 : 29 9. 18 litres of Petrol was added to a vessel containing 80 litres of Kerosene. 49 litres of the resultant mixture was taken out and some more quantity of petrol and kerosene was added to the vessel in the ratio 2:1. If the respective ratio of kerosene and petrol in the vessel was 4:1, what was the quantity of kerosene added in the vessel? A. 1 litre B. 2 litre C. 5 litre 31 | P a g e

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D. 3 litre E. None of the Above Answer & Explanation

Answer – E. None of the Above Explanation : Total quantity of the mixture = 18+80 = 98 litre quantity of petrol remaining = 18/2 = 9 quantity of kerosene remaining = 80/2 = 40 (40 + 2x) / (9 + x) = 4 / 1 x=2 Quantity of kerosene added in the vessel = 2x = 4 litre 10. A vessel which contains a mixture of acid and water in ratio 13:4. 25.5 litres of mixture is taken out from the vessel and 2.5 litres of pure water and 5 litres of acid is added to the mixture. If resultant mixture contains 25% water, what was the initial quantity of mixture in the vessel before the replacement in litres? A. 58 litre B. 68 litre C. 78 litre D. 48 litre E. None of the Above Answer & Explanation 32 | P a g e

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Answer – B. 68 litre Explanation : Quantity of Acid = 13x Quantity of water = 4x Total = 17x Resultant Mixture = 17x – 25.5 + 2.5 + 5 = 17x – 18 Resultant water = 4x – 25.5 * (4/17) + 2.5 = 4x – 3.5 Resultant mixture contains 25% water (17x – 18)*25/100 = 4x – 3.5 x=4 Initial quantity = 17*4 = 68

5.PIPES AND CISTERN 1. Three pipes A, B, and C can fill the tank in 10 hours, 20 hours and 40 hours respectively. In the beginning all of them are opened simultaneously. After 2 hours, tap C is closed and A and B are kept running. After the 4th hour, tap B is also closed. The remaining work is done by tap A alone. What is the percentage of the work done by tap A alone? A. 30 % B. 35 % C. 45 % D. 50 % E. None of the Above Answer & Explanation 33 | P a g e

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Answer – B. 35 % Explanation : Pipe A’s work in % = 100/10 = 10% Pipe B’s work in % = 100/20 = 5% Pipe C’s work in % = 100/40 = 2.5% All of them are opened for 2 hours + after 2 hours, tap C is closed + After the 4th hour, tap B is also closed = 100 => (10+5+2.5)*2 + (10+5)*2 + X = 100 => 35 + 30 + work by tap A alone = 100 => work by tap A alone = 100-65 = 35% 2. A pipe can fill a tank in 12 minutes and another pipe can fill it in 15 minutes, but a third pipe can empty it in 6 minutes. The first two pipes are kept open for 5 min in the beginning and then third pipe is also opened. Time taken to empty the water tank is? A. 30 mins B. 25 mins C. 45 mins D. 50 mins E. None of the Above Answer & Explanation

Answer – C. 45 mins Explanation : x/6 – (x+5)/12 – (x+5)/15 = 0 x = 45 mins 34 | P a g e

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3. Two pipes A and B can fill a tank in 12 hours and 18 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom of the tank it took 48 minutes excess time to fill the cistern. When the cistern is full, in what time will the leak empty it? A. 72 hours B. 62 hours C. 64 hours D. 84 hours E. None of the Above Answer & Explanation

Answer – A. 72 hours Explanation : Work done by the two pipes in 1 hour = (1/12)+(1/18) = (15/108). Time taken by these pipes to fill the tank = (108/15)hrs = 7 hours 12 min. Due to leakage, time taken = 7 hours 12 min + 48 min = 8 hours Work done by two pipes and leak in 1 hour = 1/8. Work done by the leak in 1 hour =(15/108)(1/8)=(1/72). Leak will empty the full cistern in 72 hours.

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4. A tank is normally filled in 6 hours but takes two hours longer to fill because of a leak in the bottom of the tank. If the tank is full the leak will empty it in how many hours? A. 16 hours B. 18 hours C. 17 hours D. 24 hours E. None of the Above Answer & Explanation

Answer – D. 24 hours Explanation : Work done by leak in 1 hr=(1/6-1/8)=1/24 Leak will empty the tank in 24 hours 5. Twelve pipes are connected to a Cistern. Some of them are inlet pipes and the others are outlet pipes. Each of the inlet pipes can fill the tank in 8 hours and each of the outlet pipes can empty the cistern completely in 6 hours. If all the pipes are kept open, the empty tank gets filled in 24 hours. How many inlet pipes are there? A. 6 B. 8 C. 7 36 | P a g e

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D. 4 E. None of the Above Answer & Explanation

Answer – C. 7 Explanation : (x/8)-[(12-x)/6] = 1/24 x=7 6. A dam has four inlets – A, B, C and D. The dam can be filled in 12 minutes through the first three inlets and it can be filled in 15 minutes through the second, the third and fourth inlet also it can be filled through the first and the fourth inlet in 20 minutes. How much time required to fill up the dam by all the four inlets? A. 10 mins B. 15 mins C. 20 mins D. 25 mins E. None of the Above Answer & Explanation

Answer – A. 10 mins Explanation : (1/A + 1/B + 1/C) = 1/12 …(i) (1/B + 1/C + 1/D) = 1/15 …(ii) 37 | P a g e

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(1/A + 1/D) = 1/20 …(iii) From eqn (i) and (ii) (1/A – 1/D) = 1/60…(iv) From eqn (iii) and (iv) A=30 D=60. Let the time taken to full the tank = T T(1/A + 1/B +1/C +1/D)= 1 T(1/30 + 1/15) = 1 T = 10 mins 7. Three pipes P, Q and R connected to a Cistern. The first pipe (i.e) P can fill 1/2 part of the tank in one hour, second pipe, Q can fill 1/3 part of the cistern in one hour. R is connected to empty the cistern. After opening all the three pipes 7/12 part of the cistern. Then how much time required to empty the cistern completely? A. 2 hours B. 3 hours C. 4 hours D. 5 hours E. None of the Above Answer & Explanation

Answer – C. 4 hours Explanation : In 1 hour, P can fill = 1/2 Part 38 | P a g e

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Time taken to fill the Cistern by Pipe P = 2 hours In 1 hour, Q can fill = 1/3 Part Time taken to fill the Cistern by Pipe P = 3 hours [1/2 + 1/3 – 1/R] = 7/12 1/R = 1/4 Time required to empty the Cistern = 4 hours 8. A Cistern can be filled by an inlet pipe at the rate of 4 litres per minute. A leak in the bottom of a cistern can empty the full tank in 8 hours. When the cistern is full, the inlet is opened and due to the leak, the cistern is empty in 40 hours. How many litres does the cistern hold? A. 4000 litre B. 2400 litre C. 1920 litre D. 2020 litre E. None of the Above Answer & Explanation

Answer – B. 2400 litre Explanation : Part emptied by the leak in 1 hour = 1/8 part filled by (leak & inlet open) in 1 hour = 1/40 Part filled by the inlet pipe in 1 hour = 1/8 – 1/40 = 1/10 Inlet pipe fills the tank in = 10 hours 39 | P a g e

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Inlet pipe fills water at the rate of 4 litres a minute. Capacity of Cistern = 10 * 60 * 4 = 2400 litre 9. In a tank there is a pipe which can be used for filling the tank as well as for emptying it. The capacity of the tank is 1200 m³. The emptying of the tank is 10 m³ per minute higher than its filling capacity and the pump needs 6 minutes lesser to empty the tank than it needs to fill it. What is the filling capacity of the pipe? A. 20 m³ / min. B. 40 m³ / min. C. 50 m³ / min. D. 60 m³ / min. E. None of the Above Answer & Explanation

Answer – B. 40 m³ / min. Explanation : 1200/x – 1200/(x+10) = 6 200/x – 200/(x+10) = 6 x2 + 10x – 2000 = 0 x = 40 10. Two pipes P and Q can fill a cistern in 12 hours and 4 hours respectively. If they are opened on alternate hours and if pipe A is opened first, in how 40 | P a g e

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many hours will the tank be full? A. 4 hours B. 5 hours C. 2 hours D. 6 hours E. None of the Above Answer & Explanation

Answer – D. 6 hours Explanation : Pipe P can fill = 1/12 Pipe Q can fill = 1/4 For every two hour, 1/12 + 1/4 = 1/3 Part filled Total = 6 hours

6.PATNERSHIP 1. 2 friends – A and B invested in a business by investing Rs 4000 and Rs 6000 respectively. After 8 months, A added Rs 400 more and B withdrew Rs 400. What is the profit of B from a total profit of Rs 14,250 after the end of a year? A) Rs 8,090 B) Rs 10,500 C) Rs 9,500 D) Rs 8,360 E) Rs 7,850 41 | P a g e

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Answer & Explanation

D) Rs 8,360 Explanation: A:B 4000*8 + 4400*4 : 6000*8 + 5600*4 31 : 44 So B gets = (44/75) * 14,250 2. 2 friends – A and B invested in a business by investing Rs 10,000 and Rs 12,000 respectively. After 8 months, both took out Rs 2,000. What is the profit of B from a total profit of Rs 24,800 after the end of a year? A) Rs 13,600 B) Rs 12,600 C) Rs 16,200 D) Rs 13,800 E) Rs 20,700 Answer & Explanation

A) Rs 13,600 Explanation: A:B 10000*8 + 8000*4 : 12000*8 + 10000*4 14 : 17 So B gets = (17/31) * 24,800 42 | P a g e

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3. 3 partners started a business. A, B and C invested Rs 5000, Rs 6000 and Rs 7000 respectively. After 4 months all invested the same amount as before for another 4 months. And then each of them invested Rs 1000 more. If after a year a total profit of Rs 46,500 is made, what is the profit of C? A) Rs 20,000 B) Rs 16,700 C) Rs 17,050 D) Rs 18,000 E) Rs 18,500 Answer & Explanation

D) Rs 18,000 Explanation: 5000*4 +10,000*4 + 11,000*4 : 6000*4 +12,000*4 + 13,000*4 : 7000*4 +14,000*4 + 15,000*4 26 : 31 : 36 So C gets = (36/93) * 46,500 4. The investment of A is twice as that of B and thrice as that of C. B invested for twice the months than A and thrice the months than C. Who will earn the highest profit? A) A B) B C) C 43 | P a g e

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D) Cannot be determined E) None of these Answer & Explanation

E) None of these Explanation: If A invested Rs x, then B Rs (x/2) and C invests Rs (x/3). Let B invested for y months, then A for (y/2)months, and C for (y/3) months So ratio of profit sharesA:B:C x*(y/2) : (x/2)*(y) : (x/3)*(y/3) 1/2 : 1/2 : 1/9 = 9 : 9 : 2 Both A and B gets equal and highest profits. 5. Out of the total investment, A invested 1/4th , B invested 1/3rd of the remaining and C the remaining. B earned Rs 10,000 after a year. Find the yearly profit of all. A) Rs 45,000 B) Rs 40,000 C) Rs 58,500 D) Rs 49,600 E) Rs 65,900 Answer & Explanation

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B) Rs 40,000 Explanation: Let total investment = Rs x Then A’s = (1/4)*x Remaining = 3/4th of x So B’s investment = (1/3)*(3x/4) = x/4 And C’s = x – (x/4 + x/4) = x/2 so ratio of profits = x/4 : x/4 : x/2 = 1 : 1 : 2 so 1/4 * x = 10,000 x = 40,000 6. A and B invested Rs 20,000 and Rs 25,000 in a business for 1 year and 8 months respectively. A being a working partner earned 25/3% profit out of a total profit of Rs 60,000 and after this the profit was divided in the ratio of their investments. What is the share of B in the annual profit? A) Rs 30,000 B) Rs 26,000 C) Rs 25,600 D) Rs 27,800 E) Rs 25,000 Answer & Explanation

E) Rs 25,000 Explanation: A’s share : B’s share 45 | P a g e

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20,000*12 : 25,000*8 6:5 A got its salary as = [(25/3)/100] * 60,000 = 5000 Remaining profit = 60,000 – 5000 = 55,000 So B gets = 5/11 * 55000 7. Out of a total profit of Rs 19,600, B received Rs 10,000 as his share. If A invested Rs 8,000 for 6 months while B invested his amount for 5 months, then what is the amount invested by B? A) Rs 6,000 B) Rs 8,500 C) Rs 8,500 D) Rs 10,000 E) None of these Answer & Explanation

D) Rs 10,000 Explanation: Profits ratio = 8000*6 : x*5 = 9600 : x So [x/(9600+x)] * 19,600 = 10,000 Solve, x = 10,000 8. A, B and C received their profit shares in the raio 4 : 6 : 9 respectively. A and B received a total of Rs 60,000. What is the amount that C and A got 46 | P a g e

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together? A) Rs 66,000 B) Rs 90,000 C) Rs 54,000 D) Rs 78,000 E) Rs 59,140 Answer & Explanation

D) Rs 78,000 Explanation: Their shares are 4x, 6x, 9x resp. 4x + 6x = 60,000 x = 6,000 So C got 9*6000 = 54,000 and A got 4*6000 = 24000 So total = 78,000 9. A, B and C start a business and their investments are in the ratio 4 : 3 : 6. Both A and B starts the business and C joins them after 6 months. It was decided that C will get a monthly salary of Rs 500 from the annual profits. C’s total salary came out to be 10% of the annual profit after a year. What is the share of A in the total profits? A) Rs 9,500 B) Rs 11,500 C) Rs 10,800 47 | P a g e

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D) Rs 10,000 E) Rs 12,800 Answer & Solution

C) Rs 10,800 Explanation: After a year C gets salary = 500*6 = Rs 3,000 [Since C was for 6 months in the business with each month earning 500] So 10% of total profit after a year = 3,000 Total profit = Rs 30,000 A invested for 12 months, B for 12, and C for 6 months Ratio of profit shares = 4*12 : 3*12 : 6*6 = 4 : 3 : 3 Profit left after deducting salary of C = 30,000 – 3,000 = 27,000 So share of A = [4/(4+3+3)] * 27,000 10. A, B and C invested Rs 1000 for 8 months, Rs 1200 for 6 months and Rs 1500 for some months. Out of a total profit of Rs 5,675 as profit, A received Rs 2000. For how much months did C invested? A) 7 B) 4 C) 5 D) 6 E) None of these 48 | P a g e

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Answer & Explanation

C) 5 Explanation: 1000*8 : 1200*6 : 1500*x 80 : 72 : 15x So 80/(80+72+15x) * 5675 = 2000 Solve, x = 5

7.PROBABILITY 1. A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both hearts. Find the Probability of the lost card being a heart? A. 12/50 B. 8/50 C. 11/50 D. 9/50 E. None of these Answer & Explanation

Answer – C. 11/50 Explanation : Total cards = 52 Drawn cards(Heart) = 2 Present total cards = total cards-drawn cards =52-2=50

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Remaining Card 13-2 = 11 Probability = 11/50 2. There are three boxes each containing 3 Pink and 5 Yellow balls and also there are 2 boxes each containing 4 Pink and 2 Yellow balls. A Yellow ball is selected at random. Find the probability that Yellow ball is from a box of the first group? A. 42/61 B. 45/61 C. 51/61 D. 52/61 E. None of these Answer & Explanation

Answer – B. 45/61 Explanation : Probability = (3/5 * 5/8)/([3/5 * 5/8] + [2/5 * 1/3]) = 45/61 3. A fruit basket contains 10 Guavas and 20 Bananas out of which 3 Guavas and 5 Bananas are defective. If two fruits selected at random, what is the probability that either both are Bananas or both are non-defective? A. 315/435 B. 313/435 50 | P a g e

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C. 317/435 D. 316/435 E. None of these Answer & Explanation

Answer – D. 316/435 Explanation : P(A) = 20c2 / 30c2, P(B) = 22c2 / 30c2 P(A∩B) = 15c2 / 30c2 P(A∪B) = P(A) + P(B) – P(A∩B) => (20c2/30c2)+(22c2/30c2)-(15c2/30c2)=316/435 4. A committee of five persons is to be chosen from a group of 10 people. The probability that a certain married couple will either serve together or not at all is? A. 54/199 B. 52/195 C. 53/186 D. 51/126 E. None of these Answer & Explanation

Answer – D. 51/126 Explanation : Five persons is to be chosen from a group of 10 people = 10C5 = 252 51 | P a g e

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Couple Serve together = 8C3 * 2C2 = 56 Couple does not serve = 8C5 = 56 Probability = 102/252 = 51/126 5. Out of 14 applicants for a job, there are 6 women and 8 men. It is desired to select 2 persons for the job. The probabilty that atleast one of selected persons will be a Woman is? A. 77/91 B. 54/91 C. 45/91 D. 40/91 E. None of these Answer & Explanation

Answer – A. 77/91 Explanation : Man only = 8C2 = 14 Probability of selecting no woman = 14/91 Probability of selecting atleast one woman = 1 – 14/91 = 77/91 6. Three Bananas and three oranges are kept in a box. If two fruits are chosen at random, Find the probability that one is Banana and another one is orange? A. 1/5 52 | P a g e

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B. 3/5 C. 4/5 D. 2/5 E. None of these Answer & Explanation

Answer – B. 3/5 Explanation : Total probability = 6C2 = 15 Probability that one is Banana and another one is orange = 3C1 * 3C1 = 9 probability = 9/15 = 3/5 7. A basket contains 6 White 4 Black 2 Pink and 3 Green balls. If three balls picked up random, What is the probability that all three are White? A. 4/91 B. 5/93 C. 7/97 D. 8/92 Answer & Explanation

Answer – A. 4/91 Explanation : Total Balls = 15 Probability = 6c3 / 15c3 = 4/91

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8. A basket contains 6 White 4 Black 2 Pink and 3 Green balls. If three balls are picked at random, what is the probability that two are Black and one is Green? A. 22/355 B. 15/381 C. 10/393 D. 14/455 E. 18/455 Answer & Explanation

Answer – E. 18/455 Explanation : Total Balls = 15 Probability = 4c2 * 3c1/ 15c3 = 18/455 9. A basket contains 6 White 4 Black 2 Pink and 3 Green balls. If four balls are picked at random, what is the probability that atleast one is Black? A. 69/91 B. 80/91 C. 21/91 D. 55/91 E. None of these Answer & Explanation

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Answer – A. 69/91 Explanation : Total Balls = 15 Probability = 11c4/15c4 = 22/91 One is black = 1 – 22/91 = 69/91 10. A basket contains 6 White 4 Black 2 Pink and 3 Green balls.If two balls are picked at random, what is the probability that either both are Pink or both are Green? A. 2/105 B. 4/105 C. 8/137 D. 5/137 E. None of these Answer & Explanation

Answer – B. 4/105 Explanation : Probability both are Pink = 1/15C2 Probability both are Green = 3/15C2 Required Probability = 4/15C2 = 4/105

8.PERCENTAGE 1. In a class of 60 students , 40% of the students passed in Reasoning, 5% of the students failed in Quants and Reasoning, and 20% of the students 55 | P a g e

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passed in both the subjects. Find the number of student passed only in Quants? 1.17 2.33 3.23 4.37 5.None of these Answer & Explanation

Answer – 2.33 Explanation : Total students=60 Failed in both=5% of 60=3 Passed in both=20% of 60=12 Passed in reasoning=50% of 60=24 Those passed only in reasoning =24-12=12 students. Passed only in Quants=60-(12+12+3)=33 2. The maximum marks per paper in 3 subjects in Mathematics , Physics and Chemistry are set in the ratio 1 : 2 : 3 respectively. Giri obtained 40% in Mathematics, 60% in Physics and 35% in Chemistry papers. What is overall percentage marks did he get overall? 1.44% 2.32% 3.50% 56 | P a g e

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4.60% 5.None of these Answer & Explanation

Answer – 1.44% Explanation : 40*1/100 : 60*2/100 : 35*3/100 = 0.4:1.2:1.05 Overall % =100* [0.4+1.2+1.05]/1+2+3 = 265/6 = 44.16 = 44% 3. In an examination, 50% of the students passed in Science and 75% passed in Social, while 20% students failed in both the subjects. If 270 students passed in both subjects, find the total number of students who appeared in the exam? 1.400 2.540 3.600 4.750 5.None of these Answer & Explanation

Answer – 3.600 Explanation : passed in science = 50% passed in social = 75% 20% students failed in both the subjects and 80% passed in at least one subject 57 | P a g e

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No of students passed in both subjects = 50+75−x=80 x=45% 45% of x = 270 x = 270*100/45 = 600 Total number of students =600 4. Fresh fruits contain 75% while dry fruits contain 20% water. If the weight of dry fruits is 300 kg, what was its total weight when it was fresh? 1.900kg 2.850kg 3.920kg 4.960kg 5.None of these Answer & Explanation

Answer – 4.960kg Explanation : Quantity of water in 300 kg dry fruits, = (20 /100) *300 = 60 kg Quantity of fruit alone= 300-60 =240 kg 25 kg fruit piece in 100 kg fresh fruits For 240 = (100 *240)/25 = 960 kg. 5. In a college election 35% voted for Person A, whereas 42% voted for Person B. The remaining people were not vote to any person. If the difference between those who vote for Person B in 58 | P a g e

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the election and those who are uncertain was 570, how many people are participated in the college election? 1.1500 2.2000 3.2100 4.1700 5.None of these Answer & Explanation

Answer – 2.3000 Explanation : Let the number of individuals involved in election be x. Percentage of those who were not vote = 100-(35+42) = 23% The difference between those who voted 42% of x – 23% of x = 570 19% of x = 570 x=570*100/19 = 3000 6. In a factory there are three types of bulbs L1, L2 and L3 which produces 20%, 15% and 32% of the total products respectively. L1, L2 and L3 produces 3%, 7% and 2% defective products, respectively. Find the percentage of non-defective products ? 1.46% 2.30% 59 | P a g e

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3.53% 4.64% 5.None of these Answer & Explanation

Answer – 4.64% Explanation : (20*0.97)+(15*0.93)+(32*0.98) = 19.4+13.95+31.36 = 64.71 7. In a class of 500 students ,65% are boys. 20% of the girls and 40% of the boys failed the exam.Find the of students in the school passed the exam? 1.335 2.270 3.400 4.362 5.None of these Answer & Explanation

Answer – 1.335 Explanation : Total students are 100% = 500 Boys = 65% of 500 = 325, Girls = 35% =35*500/100 =175 Girls failed in the exam= 175*80/100 = 140

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Boys failed in the exam =40/100x 325 = 195 Total = 140+195 = 335 8. The population of village increases at the rate of 6% per annum. There is an additional increase of 2% in the population due to rural development .Therefore the percentage increase in the population after 2 years will be 1.15.46% 2.16.64% 3.14.46% 4.12.56% 5.None of these Answer & Explanation

Answer – 2.16.64% Explanation : Total increase = 6+2 = 8% % increase = 8+8+(8*8/100) = 16+0.64 = 16.64% 9. The total salary of Guagn and Harish in an organization is Rs 30000. If the salary of Gugan increase by 5% and salary of Harish increase by 7%, then their total salary would increase to Rs 31800. Find the salary of Harish ? 1.Rs.10,000 2.Rs.15,000 61 | P a g e

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3.Rs.18,000 4.Rs.12,000 5.None of these Answer & Explanation

Answer – 2.Rs.15,000 Explanation : 7% increases 30000 = Rs 2100 =30000+2100 = Rs 32,100 But the actual increase in salary = 31800 Difference =32100 – 31800 = 300 2% = 300 Gugan’s salary =300/2 x 100 = 15000 Harish’s salary =30000 – 15000 = Rs 15000 10. In an examination 70% candidates passed in prelims and 55% candidates passed in Mains. If 62% candidates passed in both these subjects, then what per cent of candidates failed in both the exams? 1.37% 2.26% 3.43% 4.15% 5.None of these Answer & Explanation 62 | P a g e

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Answer – 1.37% Explanation : Students passed in Prelims = 70% Students passed in Mains = 55% Students passed in both = 62% No of students passed in at least one subject = (70+55)62 = 63%. students failed in both subjects = 100-63 = 37%.

9.TIME AND DISTANCE 1. Sofi started travelling from a place A to B and Priya started travelling from a place B to A which are 576 km apart. They meet after 12 hours. After their meeting, Sofi increased her speed by 2 km/hr and Priya reduced her speed by 2 km/hr, they arrived at B and A respectively at the same time. What is their initial speed? A. 21 kmph, 23 kmph B. 25 kmph, 27 kmph C. 25 kmph, 23 kmph D. 24 kmph, 26 kmph Answer & Explanation

Answer – C. 25 kmph, 23 kmph Explanation : Sum of their speeds = Distance/time = 576/12 = 63 | P a g e

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Quantitative Aptitude

48 kmph Respective Speed of Sofi and Priya = (25 + 23) = 48 kmph 2. A and B set out at the same time to walk towards each other respectively from a place P and Q 144 km apart. A walks at the constant speed of 8 km/h, while B walks 4 km in the first hour, 5 km in the second hour, 6 km in the third hour and so on. Then the “A” will meet “B” at? A. 36 km B. 72 km C. 56 km D. 26 km Answer & Explanation

Answer – B. 72 km Explanation : Distance travelled by them in first hour = 12 km Distance travelled by them in second hour = 13 km and so on In 9 hours both will cover exactly 144 km. In 9 hours each will cover half the total distance. 3. Two Vans start from a place with a speed of 50 kmph at an interval of 12 minutes. What is the speed of a car coming from the opposite direction 64 | P a g e

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towards the place if the car meets the vans at an interval of 10 minutes? A. 13 kmph B. 10 kmph C. 14 kmph D. 16 kmph E. None of these Answer & Explanation

Answer – B. 10 kmph Explanation : 50*12/60 = 10/60 * (50+x) 600 = 500 + 10x x = 10 kmph 4. A car travels from a place A to B in 7 hour. It covers half the distance at 30 kmph and the remaining distance at 40 kmph, what is the total distance between A and B? A. 120 Km B. 250 Km C. 240 Km D. 150 Km Answer & Explanation

Answer – C. 240 Km Explanation : 65 | P a g e

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Total Distance = x (x/2*30) +(x/2*40) = 7 x = 240 5. Two persons A and B start from the opposite ends of a 450 km straight track and run to and from between the two ends. The speed of the first person is 25 m/s and the speed of other is 35 m/s. They continue their motion for 10 hours. How many times did they pass each other? A. 1 B. 4 C. 3 D. 2 Answer & Explanation

Answer – D. 2 Explanation : First person speed = 25 m/s * 18/5 = 90 kmph Second person speed = 35 m/s * 18/5 = 126 kmph First person covers 90 * 10 = 900km 900/450 = 2 6. A truck travelled to a place Q from P, the first 50 km at 10 kmph faster than the usual speed, but it returned the same distance at 10 kmph slower than usual speed. If the total time taken by the truck is 66 | P a g e

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12 hours, then how many hours will travel at the faster speed? A. 8 hours B. 6 hours C. 2 hours D. 3 hours Answer & Explanation

Answer – C. 2 hours Explanation : Total time taken, [50/(x-10)] + 50/(x +10)] = 12 hours. By solving the equation, we get x = 15 Time is taken by the truck at faster speed = 50/(15+10) = 2 hours. 7. Mr.Kavin walks at 4/5 of his normal speed and takes 60 minutes more than the usual time. What will be the new time taken by Mr. Kavin? A. 260 minutes B. 235 minutes C. 220 minutes D. 300 minutes Answer & Explanation

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Answer – D. 300 minutes Explanation : 4/5 of speed = 5/4 of original time 5/4 of original time = original time + 60 minutes; 1/4 of original time = 60 minutes; Thus, original time = 60*4 = 240 minutes = 240 + 60 = 300 minutes 8. A travel bus normally reaches its destination at 60 kmph in 20 hours. Find the speed of that travel bus at which it travels to reduce the time by 5 hours? A. 80 kmph B. 60 kmph C. 50 kmph D. 40 kmph Answer & Explanation

Answer – A. 80 kmph Explanation : 60 * 20 = x *15 x = 80 kmph 9. A Lion starts chasing a Giraffe. It takes 4 hours to catch the Giraffe. If the speed of the Lion is 40 km/h. What is the speed of Giraffe? A. 20 km/h B. 50 km/h 68 | P a g e

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C. 40 km/h D. 70 km/h Answer & Explanation

Answer – A. 20 km/h Explanation : Giraffe Speed = x Kmph 4 = 4*x/(40-x) x = 20 km/h. 10. Anu and Purvi are running on a circular track of length 500m. The Speed of Anu is 40 m/s and that of Purvi is 30 m/s. They start from the same point at the same time in the same direction. When will they meet again for the first time? A. 25 s B. 23 s C. 50 s D. 48 s Answer & Explanation

Answer – C. 50 s Explanation : Time = Distance/Relative Speed = 500/10 = 50 s

10.TIME AND WORK

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Quantitative Aptitude

1. Arun can do a piece of work in 40 days, but Bala can do the same work in 5 days less, than Arun, when working alone. Arun and Bala both started the work together but Bala left after some days and Arun finished the remaining work in 30 days with half of his efficiency but he did the work with Bala with his complete efficiency. For how many days they had worked together? A. 25/3 days B. 31/3 days C. 35/3 days D. 38/3 days E. None of these Answer & Explanation

Answer – C. 35/3 days Explanation : 1 day work of Arun and Bala = 1/40 + 1/35 = 15/280 Arun finished the remaining work in 30 days = 30 * 1/40 * 2 = 3/8 Remaining work done by Arun and Bala = 5/8 Worked together = (5/8)/(15/280) = 35/3 days. 2. Kiran can do a work in 20 days, while Karan can do the same work in 25 days. They started the work jointly. Few days later Suman also joined them and thus all of them completed the whole work in 10 70 | P a g e

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days. All of them were paid total Rs.1000. What is the share of Suman? A. 200 B. 400 C. 100 D. 300 E. 500 Answer & Explanation

Answer – C. 100 Explanation : Efficiency of Kiran = 5% Efficiency of Karan = 4% They will complete only 90% of the work = [(5+4)*10] =90 Remaining work done by Suman = 10%. Share of Suman = 10/100 * 1000 = 100 3. 7 Indian and 4 American finish a job in 6 days. 7 African and 3 American finish the same job in 8 days. The efficiency of each person of a particular nationality is same but different from others. One Indian One American and One African will complete the work in: A. 10 days B. 12 days C. 24 days 71 | P a g e

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D. 36 days E. None of these Answer & Explanation

Answer – C. 24 days Explanation : Explanation: 7I + 4Am = 1/6 7Af + 4Am = 1/8 7I + 7Af + 7Am = 7/24 1I + 1Af + 1Am = 1/24 One Indian One American and One African will complete the work in – 24 days. 4. Chitra is twice efficient as Arun. Bala takes thrice as many days as Chitra. Arun takes 12 days to finish the work alone. If they work in pairs(i.e Arun-Bala, Bala-Chitra, Chitra-Arun) starting with Arun – Bala on the first day, Bala – Chitra on the second day and Chitra – Arun on the third day and so on, then how many days are required to finish the work? A. 26/9 days B. 46/9 days C. 16/9 days D. 56/9 days E. None of these 72 | P a g e

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Answer & Explanation

Answer – B. 9 days Explanation : No of days taken by Arun = 12 days No of days(Arun:Bala:Chitra) = 2:3:1 1 day work of (Arun+Bala) = 5/36 1 day work of (Bala+Chitra) = 8/36 1 day work of (Chitra+Arun) = 9/36 5 days total work – 35/36 1/36 is done by Arun-Chitra Number of days taken by Arun-Chitra for the rest of the work = (1/36)/(9/36) = 1/9 Total time taken to complete the work = 5 + 1/9 = 46/9 days 5. A work is done by 30 workers not all of them have the same capacity to work. Every day exactly 2 workers, do the work with no pair of workers working together twice. Even after all possible pairs have worked once, all the workers together works for six more days to finish the work. Find the number of days in which all the workers together will finish the work? A. 22 days B. 20 days C. 24 days 73 | P a g e

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D. 35 days E. 32 days Answer & Explanation

Answer – D. 35 days Explanation : 30 workers work in pairs, with no same pair of workers working together twice 29[1/w1 + 1/w2 ….. + 1/w30] + 6[1/w1 + 1/w2 ….. + 1/w30] = 1 [1/w1 + 1/w2 ….. + 1/w30] = 1/35 35 days. 6. Arun can do a piece of work in 10 days, Bala in 15 days. They work together for 5 days, the rest of the work is finished by Chitra in two more days. If they get Rs. 5000 as wages for the whole work, what are the daily wages of Arun, Bala and Chitra respectively (in Rs)? A. 600, 400, 500 B. 200, 300, 400 C. 500, 300, 400 D. 600, 500, 300 E. 400, 300, 200 Answer & Explanation

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Answer – A. 600, 400, 500 Explanation : A’s 5 days work = 50% B’s 5 days work = 33.33% C’s 2 days work = 16.66%[100- (50+33.33)] Ratio of contribution of work of Arun, Bala and Chitra = 3 : 2 : 1 Arun’s total share = Rs. 3000 Bala’s total share = Rs. 2000 Chitra’s total share = Rs. 1000 Arun’s one day’s earning = Rs.600 Bala’s one day’s earning = Rs.400 Chitra’s one day’s earning = Rs.500 7. A Contractor employed a certain number of workers to finish constructing a building in a certain scheduled time. Some time later, when a part of work had been completed, he realized that the work would get delayed by half of the scheduled time, so he at once doubled the no of workers and thus he managed to finish the building on the scheduled time. How much work he had been completed, before increasing the number of workers? A. 200/3 % B. 100/3 % C. 300/3 % D. Can’t be determined E. None of these 75 | P a g e

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Answer & Explanation

Answer – B. 100/3 % Explanation : Explanation: D * x +(100- D) * 2x= 150x => D= 50 days work done in 50 days = 50x Total work = 150x 50x/150x * 100 = 100/3 8. (x-2) person can do a work in x days and (x+7) person can do 75% of the same work in (x-10)days. Then in how many days can (x+10) person finish the work? A. 27 days B. 12 days C. 25 days D. 18 days E. None of these Answer & Explanation

Answer – B. 12 days Explanation : 3/4 * (x-2)x = (x+7)(x-10) x – 6x – 280 = 0 x = 20; x = -14 76 | P a g e

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(x-2)x = 18 * 20 = 360 360 = 30 * y y = 12 days 9. The ratio of efficiency of Arun is to Chitra is 5:3. The ratio of number of days taken by Bala is to Chitra is 2:3. Arun takes 6 days less than Chitra, when Arun and Chitra complete the work individually. Bala and Chitra started the work and left after 2 days. The number of days taken by Arun to finish the remaining work is? A. 4 days B. 5 days C. 6 days D. 9 days E. None of these Answer & Explanation

Answer – C. 6 days Explanation : Ratio of number of days = 9:10:15 Work done By B and C in first two days = 2*1/6 = 1/3 Rest of the work = 2/3 Number of days = (2/3)/(1/9) = 6 days 10. Arun is twice efficient as Bala and together they do the same work in as much time as Chitra and 77 | P a g e

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David together. If Chitra and David can complete the work in 20 and 30 days respectively, working alone, then in how many days A can complete the work individually? A. 12 days B. 18 days C. 24 days D. 30 days E. None of these Answer & Explanation

Answer – B. 18 days Explanation : 1/x + 1/2x = 1/20 + 1/30 3/2x = 1/12 Number of days taken by Arun = 18 days

11.SIMPLE INTEREST 1. Out of Rs. 60,000 that Rahul has, he lends Rs. 10,000 at 11/2 % per annum simple interest and Rs. 32,000 at 6% per annum simple interest. He lends the remaining money at a certain rate of interest so that he gets total annual interest of Rs. 4000. The rate of interest per annum, at which the remaining money is lent, is? A.5% 78 | P a g e

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B.7.5% C.8% D.8.5% E.10% Answer & Explanation

Answer –D.8.5% Explanation : Total Amount = 60000 Amount divided into three parts – x, y, z x = 10000, T = 1 yr SI(x) = (10000 * 11/2)/100 = 550 y = 32000 R = 6% SI(y) = (32000 * 6)/100 = 1920 Total Interest = 4000, Interest on the remaining amount = 4000 – 550 – 1920 = 1530 z = 60000 – 32000 – 10000 = 18000 R = (1530 * 100) /18000 = 8.5% 2. Vivek invests Rs 15000 as fixed deposit at a bank at the rate of 10% per annum SI. But due to some pressing needs he has to withdraw the entire money after 5 years, for which the bank allowed him a lower rate of interest. If he gets Rs 8250 less than what he would have got at the end of 10 years, the rate of interest allowed by the bank is A.8% 79 | P a g e

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B.8.5% C.9% D.9.5% E.10% Answer & Explanation

Answer –C.9% Explanation : P=15000, T1=10 years, T2=5 years, R1=10%, R2=? [(15000*10*10)/100 – (15000*R2*5)/100] = 8250 15000 – 750R2 = 8250 R2 = 9% 3. A father left a will of Rs.55 lakhs between his two sons aged 8.5 and 16 such that they may get equal amounts when each of them reach the age of 21 years. The original amount of Rs.55 lakhs has been instructed to be invested at 10% p.a. SI. How much did the elder son get at the time of the will? A.25 lakh B.26 lakh C.28 lakh D.33 lakh E.36 lakh Answer & Explanation

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Answer –D.33 lakh Explanation : Let x be the amount of elder son at the time of will & Younger son’s amount at the time of will (550000 -x) For elder son, T= 21-16=5 For younger son, T=21-8.5= 12.5 Amount Should be equal so, x + [(x*10*5)/100] = (5500000-x) + [((5500000x)*10*12.5)/100] 3x/2 = 12375000 – 2.25x x=3300000 4. Manish borrows 8000 at simple interest from a money lender. At the end of 3 years, he again borrows 7000 and closes his account after paying 8415 as interest after 8 years from the time he made the first borrowing. Find the rate of interest. A.6% B.6.5% C.8% D.8.5% E.9% Answer & Explanation

Answer –D.8.5% Explanation : Let x be the rate of interest 8000*3x/100 + 15000*5x/100 = 8415 81 | P a g e

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240x + 750x = 8415 X = 8.5 5. A portion of Rs.8500 is invested at a8% per annum, while the remainder is invested at a 3% per annum. If the annual income from the portion earning a 8% per annum is thrice that of the other portion, what is the total income from the two investments after one year? A.Rs.350 B.Rs.370 C.Rs.450 D.Rs.480 E.Rs.520 Answer & Explanation

Answer –D.Rs.480 Explanation : 8x + 3y = z (Total Income) x + y = 8500 -(1) 8x= 3(3y) 8x – 9y = 0 -(2) By solving (1) and (2) we get, x = 4500 so y = 4000 (4500*8*1)/100 + (4000*3*1)/100 = 360 + 120 = 480 6. Raghu lends Rs 50,000 of two of his friends. He gives Rs 30,000 to the first at 6% p.a. simple 82 | P a g e

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interest. He wants to make a profit of 10% on the whole. The simple interest rate at which he should lend the remaining sum of money to the second friend is A.8% B.16% C.11% D.17% E.19% Answer & Explanation

Answer –B.16% Explanation : S.I. on Rs 30000 =(30000×6×1)/100 = Rs. 1800 Profit to made on Rs 50000 = 50000×10/100=Rs 5000 S.I.on Rs.20000 = 5000-1800 = Rs.3200 Rate=(S.I.* 100)/(P * T)=(3200×100)/20000 =16% per annum Shortcut: 6……………………x ………..10……………. 3………………………2 4/(x-10)=2/3 x=16 83 | P a g e

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7. The rate of Simple Interest in SBI & BOB are in the ratio of 5:7. Gokul wants to deposit his total savings in two banks in such a way that he receive equal half-yearly interest from both banks.He should deposit in both banks SBI & BOB in the ratio of A.4:5 B.7:5 C.9:5 D.8:5 E.5:9 Answer & Explanation

Answer –B.7:5 Explanation : R1 =5x; R2=7x; T1=T2=1/2 yr [P1*5x*(1/2)]/100 = [P2*7x*(1/2)]/100 P1:P2 = 7:5 8. Vinay borrowed some money for one year at 8% per annum simple interest and after 18 months , he again borrowed the same money at a Simple Interest of 32% per annum. In both the cases, he paid Rs.5452. Which of the following could be the amount that was borrowed by Hari in each case if interest is paid half yearly? A.3900 B.4200 84 | P a g e

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C.4500 D.4700 E.None of the Above Answer & Explanation

Answer –D.4700 Explanation : 16% for 6 months x = Borrowed money Take x =100% 116% of x = 5452 x = 4700 9. Ravi borrows a sum of Rs.2000 at the beginning of a year. After four months Rs.2600 more is borrowed at a rate of interest double the previous one. At the end of one year, the sum of interest on both the loans is Rs.494. What is the first rate of interest per annum? A.8.5% B.9% C.9.5% D.12% E.None of the Above Answer & Explanation

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Answer –C.9.5% Explanation : P = 2000 Rate of Interest = x SI = 2000x/100 = 20x P = 2600 Rate of Interest = 2x SI = 5200x/100 = 52x 52x = 494 x = 9.5% 10. Kumar fixes the rate of interest 5% per annum for first 3 years and for the next 4 years 6 percent per annum and for the period beyond 7 years, 7.5 percent per annum. If Mr. Kumar lent out Rs.1800 for 11 years, find the total interest earned by him? A.Rs.1422 B.Rs.1242 C.Rs.1244 D.Rs.1342 E.None of the Above Answer & Explanation

Answer –B.Rs.1242 Explanation : 5% for 3 years = 15% 6% for 4 years = 24% 86 | P a g e

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7.5% for 4 years = 30% 69% of 1800 = 1242

12.AGES 1. The average runs scored by a cricketer is 42 innings, is 40. The difference between his maximum and minimum scores in an inning is 100. If these two innings are not taken into consideration, then the average score of remaining 40 inning is 37. Calculate the maximum runs scored by him in an innings? A. 125 B. 150 C. 110 D. 100 E. None of these Answer & Explanation

Answer – B. 150 Explanation : Let the minimum score = x ∴ Maximum score = x + 100

∴ x + (x + 100) = 42 x 40 – 40 x 37 ⇒ 2x + 100 = 1680 – 1480 = 200 ⇒ 2x = 200 – 100 = 100 87 | P a g e

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⇒ x = 50

Maximum score = x + 100 = 50 + 100 = 150 2. Silvia was married 8 year ago. Today her age is 9/7 times to that time of marriage. At present his son’s age is 1/6th of her age. What was her son’s age 3 year ago? A. 4 yr B. 2 yr C. 3 yr D. 5 yr E. None of the Above Answer & Explanation

Answer –B. 2 yr Explanation : Silvia’s age 8 year ago = x Present age = x + 8 x + 8 = 9/7 x 7(x + 8)= 9x x = 28; 28 + 8 = 36 Son’s age = 1/6 * 36 = 6 Son’s age 4 year ago = 6-4 =2 3. Eight years ago, Pavi’s age was equal to the sum of the present ages of her one son and one daughter. Five years hence, the respective ratio between the 88 | P a g e

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ages of her daughter and her son that time will be 7:6. If Pavi’s husband is 7 years elder to her and his present age is three times the present age of their son, what is the present age of the daughter? A. 15 years B. 23 years C. 19 years D. 27 years E. 13 years Answer & Explanation

Answer – B. 23 years Explanation : P – 8 = S + D —(1) 6D + 30 = 7S + 35 —(2) H=7+P H = 3S 3S = 7 + P —-(3) Solving eqn (1),(2) and (3) D = 23 4. Ravi’s present age is three times his son’s present age and 4/5th of his father’s present age. The average of the present ages of all of them is 62 years. What is the difference between the Ravi’s son’s present age and Ravi’s father’s present age? A. 62 years B. 64 years 89 | P a g e

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C. 69 years D. 67 years E. 66 years Answer & Explanation

Answer – E. 66 years Explanation : Present age of Ravi is = 4/5x Present age of Ravi’s father is = 4/15x Ratio = 15: 12 : 4 Difference between the Ravi’s son’s present age and Ravi’s father’s present age = 62/31 * 3(15 – 4). = 2*3*11 = 66 year. 5. The respective ratio between the present age of Mary and Deepa is x : 42. Mary is 8 years younger than Prema. Prema’s age after 8 years will be 33 years. The difference between Deepa’s and Mary’s age is same as the present age of Prema. What is the value of x? A. 18 B. 10 C. 16 D. 11 E. 17 Answer & Explanation 90 | P a g e

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Answer – E. 17 Explanation : Prema’s age after 8 years = 33 years Prema’s present age = 33 – 8= 25 years Mary’s present age = 25 – 8 = 17 years Deepa’s present age = 17 + 25 = 42 years Ratio between Mary and Deepa = 17 : 42 X = 17 6. Mr. Sharma has three sons namely Ram, Amit and Karan. Ram is the eldest son of Mr. Sharma while Karan is the youngest one. The present ages of all three of them are square numbers. The sum of their ages after 5 years is 44. What is the age of Ram after three years? A. 15 years B. 13 years C. 19 years D. 17 years E. 16 years Answer & Explanation

Answer – C. 19 years Explanation : Square numbers – x, y, z (x + 5) + (y + 5)+ (z + 5) = 44 x + y + z = 44 – 15 = 29 91 | P a g e

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Possible values of x, y, z = 4, 9, 16 [Out of 1, 4, 9, 16, 25] Ram’s present age = 16; after three years = 19 7. One year before, Reshma was six times as old as her daughter. Six years hence, Reshma’s age will exceed her daughter’s age by 20 years. The ratio of the present ages of Reshma and her daughter is? A. 5 : 4 B. 9 : 4 C. 5 : 1 D. 7 : 2 E. None of the Above Answer & Explanation

Answer – C. 5 : 1 Explanation : Ages of Reshma and her daughter = 6x, x [6x + 1 + 6] – [x + 1 + 6] = 20 5x = 20; x = 4 Ratio = 6x + 1 : x + 1 = 25 : 5 = 5:1 8. The ratio of present ages of Ramya and Karan’s age is 4:5 and the ratio of present ages of Karan and Priya is 2:5 respectively. If Ramya is two-fifth of Priya’s age, What is Ramya’s age? A. 12 years B. 10 years 92 | P a g e

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C. 20 years D. Cannot be determined E. None of the Above Answer & Explanation

Answer – D. Cannot be determined Explanation : Data Insufficient – Can not be determined. 9. Ravi is as much younger than Surya as he is older than Suresh. If the sum of the ages of Surya and Suresh is 50 years, what is definitely the difference between Surya and Ravi’s age? A. 12 years B. 23 years C. 19 years D. 27 years E. Can not be determined Answer & Explanation

Answer – E. Can not be determined Explanation : Surya’s age – Ravi’s age = Ravi’s age – Surya’s age Suresh’s age + Surya’s age = 2 Ravi’s age Surya’s age + Suresh’s age = 50 Ravi’s age = 25; We can not find the difference between Surya and Ravi’s age 93 | P a g e

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10. Amit’s present age is 1.5 times of Hari’s present age. If after 4 years, Amit’s age will be twice of Hari’s age 4 years ago. What is the sum of the present ages of Amit and Hari? A. 52 years B. 53 years C. 60 years D. 67 years E. 63 years Answer & Explanation

Answer – C. 60 years Explanation : A = 1.5 * H A + 4 = 2 * (H – 4) A + 4 = 2H – 8 A + 12 = 2H 1.5H + 12 = 2H H = 24 A = 24 * 1.5 = 36 Sum = 36 + 24 = 60

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