# Aptitude model placement papers with solution - set 2

## Aptitude model placement papers with solution - set 2

Q1. A boat has a speed of 14kmph in standing water. The stream has a speed of 1.2kmph. What time does the boat take to go to a distance of 4864 km and come back? (hours)

A. 700
B. 350
C. 1000
D. 4200

Solution: A boat travels at the speed of 14 km/hr in still water.

=> Speed of stream = 1.2 kmph

=> Speed of boat downstream becomes 14 + 1.2 = 15.2 kmph

=> Speed of boat upstream becomes 14 - 1.2 = 12.8 kmph

Total time taken in the journey = Journey downstream + Journey upstream

Therefore, 4864(1/12.8 + 1/15.2) = 700 hours

Q2. In how many different ways can a group of 4 be made out of 4 girls and 6 boys such that at least one boy is selected each time?

A. 159
B. 209
C. 201
D. 212

Solution: This solution can be determined by 2 ways. Include at least one boy in each group and make 4 cases. A simpler way would be finding out total ways of selecting 4 people from the total group and subtracting the case with no boy.

=> Group of 4 out of 10 children - Group of 4 out of 4 girls.

=> 10C4 - 4C4

=> 210 - 1

=> 209

Q3. 20% of A is B, then B% of 20 is same as what?

A. 4% of A
B. 10% of A
C. 20% of A
D. None

Solution: It is given that B measures 20% of A

=> So, 20% of A = B or 20/100 * A = B - (1)

B% of 20= B/100 X 20= 2B/10 ---(2)

=> Now, B% of 20

Substituting (1) in (2) we get

2*(2A/10) / 10= 4A/100

Hence, B% of 20 = 4% of A

Q4. With an investment of 45000, X starts a business which is joined by Y after 3 months with 30000. How should they share the profit at the end of the year?

A. 1:3
B. 2:1
C. 1:3
D. 3:1

Solution: Let us consider the relationships here:

Time and Profit ---------------Direct Relationship ---- More time More profit

Investment & Profit ------Direct Relationship ---- More investment More profit

Ratio of profit = Investment * Time of Investment

= 45000 * 12 : 30000 * 9

= 2:1

Q5. A container has 40L milk. 4L milk is taken out and replaced with water, the process done three times. What is the amount of milk now left?

A. 28L
B. 29L
C. 29.16L
D. 28.4L

Solution: In regard to the problem let after n times liquid in the container is x and liquid removed is y

=>Liquid in container= x

=>Liquid removed= y

After one trial, quantity of pure liquid= x- (1-y/x)

After n trials quantity of pure liquid = x - (1 -y/x)n

Therefore, Putting the values ( x = 40L y = 4L N=3) and solving

=> 40- (1-4/40)3

= 29.16L

Q6. The cost price of a particular amount of articles is same as the number of articles. Selling price of the articles comes out to be 20. Over the whole transaction 25% is gained. What is X?

A. 15
B. 18
C. 16
D. 20

Solution: According to the question let n be the number of articles.

=> Cost price of n articles = n

=> Selling price of n articles = 20

=> Profit % = 25%

=> Profit % = (SP - CP)/CP X 100

Putting the values in the formula

(20-n)/n x 100 = 25

=> 5n/4 = 20

=> n = 16

Q7. Three coins are tossed. What is the probability of getting at most two tails?

A. 7/8
B. 1/8
C. 2/8
4. 4/8

Solution: It is given that 3 coins are tossed simultaneously.

=>Total outcomes when one coin is tossed=2

=>Total outcomes when 3 coins are tossed= 2n = 2 X 2 X 2

=8 outcomes

Favourable outcomes: TTH, THT, HTT, THH, THT,HHT,HHH=7

Therefore, Probability= 7/8

Q8. A pump fills a tank in 2 hours. Due to a leak it took 2 2/3 hours to fill the tank. In how much time will the leak drain the entire tank?

A. 6 hours
B. 8 hours
C. 9 hours
D. 10 hours

Solution: It is given that tank is filled in 2 hours. Let tank drain out in y hours

=> Part of the tank filled in one hour = 1/2
=> Part emptied in one hour by leak = 1/y
=>Part filled in one hour following leak = 1/ (8/3)

In one hour: 1/2 - 1/7 = 3/8

Therefore, Solving for y, y=8

Q9. For a race a distance of 224 meters can be covered by P in 28 seconds and Q in 32 seconds. By what distance does P defeat Q eventually?

A. 26m
B. 32m
C. 24m
D. 28m

Solution: This is a simple speed time problem. Given conditions:

=>Speed of P= 224/28 = 8m/s

=>Speed of Q=224/32 = 7m/s

=>Difference in time taken = 4 seconds

Therefore, Distance covered by P in that time= 8m/s x 4 seconds = 32 metres