# Aptitude model placement papers with solution - set 6

## Aptitude model placement papers with solution - set 6

1. 12 men and 18 boys working 7.5 minutes an hour complete a particular piece of work in 60 hours. If a boy’s work is half as efficient as a man’s work, how many boys will be needed to help 21 men to achieve twice the work in 50 hours working 9 minutes in an hour.

A. 42
B. 46
C. 48
D. 38

Solution: 1 man is equivalent to 2 boys in work capacity. 12 men + 18 boys = 12 x 2 + 18 = 42 boys.

Let the required number of boys be x. So Total number of people doing work = 21 men x 2 (according to work capacity) + x boys.

Taking respective ratios as required:

Given:

=> Hours 50:60
=> Minutes per hour 9: 15/2
=> Work 1:2
=> People: 42: 42 + x
=> 50 x 9 x 1 x (42+x) = 60 x 15/2 x 2 x 42
=> 42 +x = 84

x = 42

2. Two pipes A and B can fill a cistern in 37.5 minutes and 45 minutes respectively. This cistern will be filled in half an hour if both the pipes are opened together initially and pipe B is then turned off after X minutes. What is X?

A. 10 minutes
B. 15 minutes
C. 12 minutes
D. 9 minutes

Solution: Let B be turned off after X minutes.

Part of water will be filled by A + B in x minutes + After tap B is closed rest filled by A in (30-x) minutes = 1

=> x/(time taken to fill the container by each separately) + 30 - x/(time taken to fill the container by A alone) = 1
=> x(2/75 + 1/45) + (30-x)2/75 = 1
=> 11x + 180 – 6x = 225

Therefore, x = 9 minutes

3. A starts walking at 4 kmph and 4 hours after his start B starts cycling at 10 kmph. After how much distance will B catch up with A?

A. 26.2 km
B. 25.7 km
C. 23.2 km
D. 26.67 km

Solution: Distance travelled by each of them is to be made equal.

=> Distance travelled walking = Distance covered cycling.

Let after 4 hours of walking, A walk for x hours more before B catches up with him.

=> Distance = Speed * Time

(4+x)4 = 10x

x = 8/3

Therefore, It takes B 8/3 hours to catch up with A. Distance: 8/3 x 10 = 80/3 km = 26.67

4. A man can row a boat three quarters of a kilometre in 11.25 minutes. What is the speed of the boat in still water?

A. 2 kmph
B. 5 kmph
C. 4 kmph
D. 3 kmph

Solution: Simple Division.
No stream current mentioned.
Trick question.
Speed= Distance/Time.
Speed= 3/4 km / (11.25/60) hr
Therefore, Speed = 4 km/hr

5. 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

Solution: Let initial amount that the man invests be A

Let 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 = 561

Therefore, a = 6600

6. A sum of money becomes Rs 13,380 in 3 years and Rs 20,070 in 6 years at compound interest. The initial sum is?

A. Rs 9040
B. Rs 8900
C. Rs 8920
D. Rs 9160

Solution: Use the formula Amount = Principal Amount(1 + R/100)n

Where r is rate and t is time in years

=>13,380 = P(1+R/100) 2 --(1)

=>20,070 = P(1+R/100) 6 --(2)

=> 1.5 = (1+R/100) 4

=> P = Rs 8920

7. A square, a circle and an equilateral triangle have equal perimeters. If T represents the triangle, S the square and C the circle determine the relationship in their areas:

A. S < T < C
B. T < S < C
C. C < S < T
D. T < C < S

Solution: Let a be the side of square b be the side of triangle and r be the radius of the circle:

It is given that perimeter of all the three figures is same
=> 4a = 3b = 2πr
=> a = 3b/4
=> r= 3b/2π

Areas: Now that we have all the three sides in terms of b we can equate and compare areas of the three equations:

Square: 9b2/16
Triangle: b2/4
Circle: 9b2/4π

From this we can say that Area (Circle) > Area (Square) > Area (Triangle)

8. 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%

Solution: Let old radius be 1r

As the radius has increased by 6%, the new radius = 1.06 r

New area = π (1.06r)2
=1.1236πr2

Increase: πr2 (1.1236) - πr2

=> 0.1236πr2 /πr2

=> 12.36%

9. 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

Solution: 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)/3

x = 4.6

10. Determine the odd man out:

15, 16, 34, 105, 424, 2124

A. 105
B. 424
C. 34
D. 2124

Solution: The following pattern has been followed in this question:

16 = 15 x 1 + 1

34 = 16 x 2 + 2

We 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 + 3

424 = 105 x 4 + 4

2125 = 424 x 5 + 5

=> 2124 is incorrect