# Aptitude test series Set 5

1)   A man invests 1/3rd of his income at 7%, 1/4th at 8% and the remainder of his income at 10%. If the annual profit is Rs 561. What was the initial capital?

a. Rs 7500
b. Rs 6600
c. Rs 4500
d. Rs 3000
 Answer  Explanation ANSWER: Rs 6600 Explanation: Let initial amount that the man invests be ALet x be the capital=> Profit on 1st investment + Profit on 2nd investment + Profit on 3rd investment => S.I. = P X R X T=> Remainder of capital = 1 - 1/3 - 1/4 = 5/12x (x being the capital)=> a*1/3 *7/100 + 1/4 *a * 8/100 + 5x/12*a* 10/100 = 561Therefore, a = 6600

2)   What is the angle between the hour and minute hand at 3:40?

a. 135
b. 130
c. 120
d. 125
 Answer  Explanation ANSWER: 130 Explanation: When minute hand is behind the hour hand, the angle between the minute hand and hour hand at M minutes past H hours is given by:=> 30 * (H-M/5) + M/2When minute hand is ahead of hour hand, the formula becomes:=> 30* (M/5-H) – M/2Applying the second formula as here the minutes hand is ahead of the hour hand.=> 30* (40/5-3) – 40/2=> 30* (8-3) – 20=> 30*5 – 20=> 150-20=> 130Thus the angle formed is 130 degrees.

3)   A jar is filled of liquid which is 3 parts water and 5 parts alcohol. How much of this mixture should be drawn out and replaced such that this mixture may contain half
water and half alcohol?

a. 25%
b. 20%
c. 14.29%
d. 33.33%
 Answer  Explanation ANSWER: 20% Explanation: Let the jar initially contain 8 litres of mixture:3 litres water and 5 litres alcoholLet x litres of this mixture is drawn out and is replaced by x litres of water.Amount of water now in the solution: 3-(3/8)x+x.Amount of alcohol now in the solution: 5-(5/8)xDesired ratio: 1/1=>3-(3/8)x+x=5-(5/8)xx=8/5 litres%x=((8/5)/8)*100=20%

4)   Two trains each of which is 100 m long moving in opposite direction to one another cross each other taking 8 seconds. If speed of one train is twice the speed of other
train find the speed of the faster train.

a. 48 km/hr
b. 30 km/hr
c. 60 km/hr
d. 40 km/hr
 Answer  Explanation ANSWER: 60 km/hr Explanation: No explanation is available for this question!

5)   Think of a number, divide it by 4 and add 9 to it. The result is 15. What is the number thought of?

a. 24
b. 25
c. 26
d. 27
 Answer  Explanation ANSWER: 24 Explanation: No explanation is available for this question!

6)   Total age of A and B is 12 years more than the total age of B and C. By how many years is C younger than A?

a. 12 years
b. 24 years
c. Data insufficient
d. None of these
 Answer  Explanation ANSWER: 12 years Explanation: No explanation is available for this question!

7)   If x + 5y = 16 and x= -3y, then y =

a. -24
b. -8
c. 8
d. 2
 Answer  Explanation ANSWER: 8 Explanation: No explanation is available for this question!

8)   A, B and C distribute Rs. 1,000 among them. A and C have Rs. 400, B and C Rs. 700. How much does C have?

a. Rs 100
b. Rs 50
c. Rs 200
d. Rs 300
 Answer  Explanation ANSWER: Rs 100 Explanation: No explanation is available for this question!

9)   a:b = 5:2. What is the value of (8a + 9b): (8a + 2b)?

a. 22:29
b. 26:61
c. 29:22
d. 61:26
 Answer  Explanation ANSWER: 29:22 Explanation: No explanation is available for this question!

10)   A class consists of 15 girls and 10 boys. Three students are to be randomly selected. Find the probability that one boy and two girls are picked.

a. 1/50
b. 3/25
c. 21/46
d. 25/122
 Answer  Explanation ANSWER: 21/46 Explanation: No explanation is available for this question!

11)   The third proportional to x2-y2, x-y is?

a. x + y
b. x – y
c. x – y/(x + y)
d. 1
 Answer  Explanation ANSWER: x – y/(x + y) Explanation: A simple problem involving geometric progression (G.P)In each term, a term of (x + y) is divided. Hence the third term becomes x-y/(x+y)

12)   Determine the odd man out:

15, 16, 34, 105, 424, 2124

a. 105
b. 424
c. 34
d. 2124
 Answer  Explanation ANSWER: 2124 Explanation: The following pattern has been followed in this question:16 = 15 x 1 + 134 = 16 x 2 + 2We have established that previous number is multiplied by increasing numbers (1,2,3,4.....) and then added by increasing numbers (1,2,3,4...)105 = 34 x 3 + 3424 = 105 x 4 + 42125 = 424 x 5 + 5=> 2124 is incorrect

13)   India has a run rate of 3.2 in the first 10 overs. What should be the run rate in remaining 40 overs to win a game of 282 runs?

a. 6.25
b. 5.5
c. 7.25
d. 8
 Answer  Explanation ANSWER: 6.25 Explanation: Runs scored in first 10 overs: => Rate*Overs= 3.2*10 = 32 runs=> Required runs = 282-32 = 250=> Left overs= 40Required rate = runs/overs= 250/40= 6.25=> 6.25 runs per over is needed to win the game.

14)   A man cycles at a rate of 4 kmph. He cycles for 45 minutes and then takes a 15 minute break. Determine the total time taken to cover 12 kms by him.

a. 4 hours 35 minutes
b. 4 hours
c. 3 hours
d. 3 hours 45 minutes
 Answer  Explanation ANSWER: 3 hours 45 minutes Explanation: Speed of man = 4kmphTime for which he cycled = 45 minutes.Distance covered = speed*time=> 4*45/60=> 3kmTotal time to cover 3 km = 45 minutes + 15 minutes = 60 minutes = 1 hourThus 3 km is covered in 1 hourRequired distance to be covered = 12 kmBeginning from origin point, he covers 9 km in 3 hours taking 15 minutes rest after every 45 minutes. To complete 12 kms he goes another 3 km in 45 minutes. Thus, total time he takes is 3 hours 45 minutes.

15)   Two pipes A and B can fill a tank in 12 and 24 minutes respectively. If both the pipes are used together, how long will it take to fill the tank?

a. 9 min
b. 8 min
c. 4 min
d. 6 min
 Answer  Explanation ANSWER: 8 min Explanation: Tank can be filled by pipe A in 12 minutes and pipe B in 24minutes.=> Part filled by A in 1 minute= 1/12=> Part filled by B in 1 minute= 1/24=> Part filled by both in 1 minute= 1/12 + 1/24= 3/24=1/8Time taken to fill the entire tank = 8 minutes

16)   Radius of a circle is increased by 6%, determine the increase in area of the circle.

a. 12%
b. 12.36%
c. 12.64%
d. 6%
 Answer  Explanation ANSWER: 12.36% Explanation: Let old radius be 1rAs the radius has increased by 6%, the new radius = 1.06 rNew area = π (1.06r)2=1.1236πr2 Increase: πr2 (1.1236) - πr2=> 0.1236πr2 /πr2=> 12.36%

17)   FIND THE ODD NUMBER:

1,5,11,17,23,29

a. 29
b. 17
c. 11
d. 1
 Answer  Explanation ANSWER: 1 Explanation: All the given numbers are prime numbers.1 is not a prime number because it is divisible by only one factor that is 1.

18)   Average of six numbers comes out to be 3.95. Average of two of the numbers is 3.4 while the average of other two is 3.85. Determine the average of the two numbers left.

a. 4.7
b. 4.8
c. 4.3
d. 4.6
 Answer  Explanation ANSWER: 4.6 Explanation: In the given question we have taken average of 6 numbers taken 2 at a time which makes 3 numbers.=> 3.95 (Average of 1st and 2nd number) => 3.85 (Average of 3rd and 4th number)=> 3.4 (Average of 5th and 6th number)3.95 = (3.4 + 3.85 + x)/3x = 4.6

19)   In a group containing 6 cows and 4 buffalos, 4 livestock are to be selected in such a way that at least 1 cow should always be present. How many way of doing that are possible?

a. 209
b. 205
c. 194
d. 163
 Answer  Explanation ANSWER: 209 Explanation: No explanation is available for this question!

20)   What is the smallest number which is a perfect square and is divisible by 16, 20 and 24?

a. 2400
b. 3600
c. 7200
d. 1600
 Answer  Explanation ANSWER: 3600 Explanation: 3600. The number is perfect square of 60.It is divisible by 36 24 and 20. Only two numbers 3600 and 7200 fit these conditions.It is clear that 3600 is the smaller number.