# Aptitude test series Set 7

1)   36 is divided in 2 parts such that 8 times the first part added to 3 times the second part makes 203. What is the first part?

a. 15
b. 19
c. 23
d. None of these
 Answer  Explanation ANSWER: 19 Explanation: Let the first part be x.8x + 3 (36 – x) = 2038x + 108 – 3x = 2035x + 108 = 2035x = 95x = 19

2)   The least number which is a multiple of 11 and when divided by 3, 5 and 9 leaves 2 as remainder:

a. 297
b. 319
c. 407
d. None of these
 Answer  Explanation ANSWER: 407 Explanation: The L.C.M. of 3, 5 and 9 is 45.Hence, the number is of the form (45a + 2).The least value of ‘a’ for which (45a + 2) is multiple of 11 is 9.Therefore, the number is 407.

3)   What is the fourth proportional to the numbers 2, 5, 8.

a. 40
b. 20
c. 15
d. 10
 Answer  Explanation ANSWER: 20 Explanation: 2/5 = 8/x ; x = 40/2 = 20

4)   Find the value of x when y = 5, if x varies directly as 4y-1 and x = 14 when y = 2.

a. 38
b. 35
c. 10
d. 28
 Answer  Explanation ANSWER: 38 Explanation: Let z = 4y-1When x = 14, y = 2, z = (4*2) – 1 = 7Now, x varies directly as z = 4y-1When y = 5, z = (4*5) – 1 = 19x 14 7 y - 19Therefore, x = (14*19)/7 = 38

5)    If a cloth merchant sells ‘a’ metres of cloth for Rs.x, then what is the selling price of ‘b’ metres of cloth?

a. Rs.(b*x)
b. Rs.{(b*x)/a}
c. Rs.{(a*b)/x}
d. None of these
 Answer  Explanation ANSWER: Rs.{(b*x)/a} Explanation: Cost of ‘a’ metres of cloth = Rs.x. Therefore, each metre of cloth costs Rs. (x/a). The cost of ‘b’ metres of cloth = Rs. b*(x/a) = Rs. {(b*x)/a}

6)   A leak at the bottom of the tank can empty the tank in 5 hours, while an inlet pipe can fill the same tank at the rate of 6 litres per minute. When the tank is full, the inlet is opened and the tank gets empty in 8 hours due to the leakage. Find the capacity of the tank.

a. 1800 litres
b. 3600 litres
c. 4800 litres
d. 5760 litres
 Answer  Explanation ANSWER: 4800 litres Explanation: The capacity of the tank is given by C = (p*q*r)/(r – p) litresWhere, p = time in which the leakage can empty the tank in hours = 5 hoursq = rate at which the inlet fills the tank in lph = 6*60 = 360 lphr = time in which the tank gets emptied in hours = 8 hoursHence, C = (5*360*8)/(8 – 5)C = 4800 litres

7)   Vessel ‘A’ contains 150 litres of mixture of milk and water in the ratio of 3:1. Vessel ‘B’ contains 200 litres of the mixture in the ratio of 5:2. If the mixture from both the vessels are poured into vessel ‘C’, find the ratio of the resulting mixture.

a. 15 : 7
b. 8 : 3
c. 15 : 2
d. 143 : 53
 Answer  Explanation ANSWER: 143 : 53 Explanation: As vessel A contains 150 litres of mixture of milk and water in the ratio 3:1, the quantity of milk is 3*150/4 litres, and that of water is 150/4 litres.Similarly, as vessel B contains 200 litres of mixture of milk and water in the ratio 5:2, the quantity of milk is 5*200/7, and that of water is 2*200/7 litres.After mixing the total quantity is 350 litres.The quantity of milk is {(3*150/4) + (5*200/7)} = 7150/28The quantity of water is {(150/4) + (2*200/7)} = 2650/28The ratio of the resulting mixture = 7150/2650 = 143 : 53

8)    If Ajay drives at 4/5th of his usual speed to his office, he is 6 minutes late. What is his usual time to reach his office?

a. 36
b. 24
c. 30
d. 18
 Answer  Explanation ANSWER: 24 Explanation: Let t be his usual time to reach his office and v be his usual speed.v = d/t ……….(d is the distance Ajay travels while going to his office)vt = dAt v1 = 4v/5 ; t1 = t + 64v/5 = d/(t + 6)4v/5* (t + 6) = d4v/5* (t + 6) = vtOn solving we get,t = 24 minutes

9)   If a boat is rowed downstream for 50 km in 5 hours and upstream for 24 km in 6 hours, what is the speed of the boat and the river?

a. (7 , 3) km/hr
b. (6 , 4) km/hr
c. (10 , 4) km/hr
d. None of these
 Answer  Explanation ANSWER: (7 , 3) km/hr Explanation: If x: speed of boats man in still watery: speed of the riverDownstream speed (Ds) = x + yUpstream speed (Us) = x – yx = (Ds + Us) / 2y = (Ds – Us) / 2In the above problem Ds = 10 ; Us = 4x = (10 + 4) / 2 = 14/2 = 7 km/hry = (10 - 4)/2 = 6/2 = 3 km/hr

10)   If Ajay completes a certain work in 8 days and Vijay can complete the same work in 24 days, find the time in which the work will be completed if both Ajay and Vijay work together.

a. 12 days
b. 16 days
c. 6 days
d. 10 days
 Answer  Explanation ANSWER: 6 days Explanation: On working together Ajay and Vijay can complete the work in (8*24)/(8 + 24)= 192/32= 6 days

11)   What fraction is equivalent to 0.8% ?

a. 1/125
b. 2/25
c. 4/5
d. None of these
 Answer  Explanation ANSWER: 1/125 Explanation: 0.8% = 0.8/100 = 8/1000 = 4/500 = 2/250 = 1/125

12)   Akshay buys a motorcycle for Rs.25000. If he decides to sell the motorcycle for a profit of 7%, find the selling price.

a. 27000
b. 26750
c. 26000
d. 25750
 Answer  Explanation ANSWER: 26750 Explanation: Profit = %profit/100 * cost priceP = 7/100 * 25000 = 1750.Selling price = cost price + profit= 25000 + 1750= Rs.26750

13)   Vijay says that his weight is between 75kg and 85 kg. But his younger sister disagrees with Vijay and says that his weight is greater than 70kg but less than 80 kg. Vijay’s mother says that his weight cannot be greater than 78 kg. If all the three predictions are correct, what is the average of different probable weights of Vijay?

a. 75
b. 80
c. 78.5
d. 76.5
 Answer  Explanation ANSWER: 76.5 Explanation: Vijay’s opinion: - 75 < Vijay’s age < 85Sister’s opinion: - 72 < Vijay’s age < 82Mother’s opinion: - Vijay’s age < 78As all the above three conditions are true, the values satisfying them are 76 & 77.Average value = (76 + 77)/ 2 = 76.5

14)   If the ratio of the ages of Shweta and Veena was 5:6 six years ago and it will become 10:11 in 4 years from now, then find the present age of Veena.

a. 16
b. 18
c. 10
d. 12
 Answer  Explanation ANSWER: 18 Explanation: Let the ages of Shweta and Veena 6 years ago be 5x and 6x.Present ages is (5x + 6) and (6x +6) respectively, and their ages 4 years from now will be (5x + 10) and (6x + 10).(5x + 10) / (6x + 10) = 10 /1155x + 110 = 60x + 1005x = 10x = 2Present age of Veena = (6x + 6) = (6*2 + 6) = 18 years

15)   If the length is increased by 25%, by what percent the width of a rectangle should be decreased so as to keep the area same.

a. 25%
b. 20%
c. 30%
d. 10%
 Answer  Explanation ANSWER: 20% Explanation: Let the original length be l and the width be bTherefore, the area = l*bNow, as the length is increased by 25%, the new length is (1.25*l) and let the new width be x.As the area is same, 1.25*l*x = l*bx = b/1.25 = 0.8bTherefore, the width is to be decreased by 20%.

16)   A company pays 12.5% dividend to its investors. If an investor buys Rs.50 shares and gets 25% on investment, at what price did the investor buy the shares?

a. 6.25
b. 25
c. 50
d. 12.5
 Answer  Explanation ANSWER: 25 Explanation: Dividend on 1 share = (12.5 * 50)/100 = Rs.6.25Rs.25 is income on an investment of Rs.100Rs.6.25 is income on an investment of Rs. (6.25 * 100)/25 = Rs.25

17)   In how many different ways can the letters of the word ‘GEOMETRY’ be arranged so that the vowels always come together?

a. 720
b. 4320
c. 2160
d. 40320
 Answer  Explanation ANSWER: 4320 Explanation: There are in all 8 letters in the given word of which 3 are vowels. As the vowels should always be together, considering the 3 vowels as one letter, there are in all 6 letters which can be arranged in 6! ways = 720Also the 3 vowels can be arranged in 3! ways = 6Total number of arrangements = 720*6 = 4320

18)   Tickets numbered 1 to 50 are mixed and one ticket is drawn at random. Find the probability that the ticket drawn has a number which is a multiple of 4 or 7?

a. 9/25
b. 9/50
c. 18/25
d. None of these
 Answer  Explanation ANSWER: 9/25 Explanation: S = {1, 2, 3, … , 49, 50}E = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 7, 14, 21, 35, 42, 49}n(S) = 50n(E) = 18P(E) = n(E)/n(S) = 18/50 = 9/25

19)   Rashmi and Rakhi were partners in a business. Rashmi contributed 2/3rd of the capital for 20 months and Rakhi received 3/5th of the total profit. What was the time duration of Rakhi’s investment in the business?

a. 45 months
b. 30 months
c. 60 months
d. 10 months
 Answer  Explanation ANSWER: 60 months Explanation: Ratio of the capital = 2 : 1Ratio of the profit = 2 : 3Let the duration of Rakhi’s investment be x months.(2*20) : (1*x) = 2 : 3x = 60 months

20)   34, 45, 56, 67,78, _ ?

a. 81
b. 83
c. 89
d. None of these
 Answer  Explanation ANSWER: 89 Explanation: No explanation is available for this question!

21)   CX, EV, GT, IR, ?

a. JQ
b. LO
c. KP
d. MN
 Answer  Explanation ANSWER: KP Explanation: No explanation is available for this question!

22)   5, 25, 61, 113, ?

a. 187
b. 189
c. 185
d. 181
 Answer  Explanation ANSWER: 181 Explanation: No explanation is available for this question!

23)   1, 9, 17, 33, 49, 73, _ .

a. 98
b. 97
c. 89
d. 90
 Answer  Explanation ANSWER: 97 Explanation: No explanation is available for this question!

24)   How much time does a train 125 metres long running at 60 km/hr take to pass a pole?

a. 6s
b. 2.08s
c. 7.5s
d. 8s
 Answer  Explanation ANSWER: 7.5s Explanation: 60 km/hr = 60 * 5/18 = 16.67 m/sSpeed = distance/time; v = d/t16.67 = 125/tt = 7.5s

25)   If a pipe can fill a tank in 6 hours, find the part of tank it fills in one hour.

a. 1/6
b. 2/3
c. 1/2
d. None of these
 Answer  Explanation ANSWER: 1/6 Explanation: Let the capacity of the tank be C litres.Time to fill the tank = 6 hoursHence, in 1 hour C/6 litres gets filled.Therefore, 1/6th part of the tank gets filled in one hour.

26)   A group of 55 adults and 70 children go for trekking. If there is meal for either 70 adults or 90 children and if 28 adults have their meal, find the total number of children that can be catered with the remaining food.

a. 42
b. 54
c. 90
d. 70
 Answer  Explanation ANSWER: 54 Explanation: As there is meal for 70 adults and 28 have their meal, the meal left can be catered to 42 adults. Now, 70 adults = 90 children 7 adults = 9 children Therefore, 42 adults = 54 children Hence, the meal can be catered to 54 children.