# Chain Rule - Aptitude Questions and Answers Part 2

6. Ram and Shyam take a project to work together. However, Shyam falls sick after working for 20 days and Ram works alone on the project for last 6 days. They submit the project in 26 days. Had Ram and Shyam worked on the project for all the days together, they could have submitted it in 24 days. How many days will Shyam take to complete the project alone?

a. 13 days
b. 36 days
c. 52 days
d. 72 days

Explanation:

 Let work done by Ram in 1 day = 1 & by Shyam in 1 day = 1 R S
 Both complete work in 24 days. So in 1 day, together they complete = 1 = 1 + 1 24 R S
 For 20 days both work together, so work done by them = 20 1 + 1 = 5 R S 6
 Remaining work 1 - 5 = 1 is done by Ram alone in 6 days 6 6
 Work done by Ram in 6 days = 1 = 6 1 6 R
∴ R = 36 = days needed by Ram to complete the work alone
 ∴ 1 + 1 = 1 36 S 24
∴ S = 72 = days needed by Shyam to complete the work alone

7. No. of books bound by a child is half the number of books a man can bind. 20 men and 16 children take 10 days to bind all the books. If there are 8 men and 12 children working on the assignment, how many days will they take to bind all the books?

a. 20 days
b. 24 days
c. 25 days
d. 40 days

Explanation:

Tip:
Men = M; Days = D; Time/Hours = T; Work = W
M1D1T1W2 = M2D2T2W1
Note that - W2 is on left side and W1 is on right side

1 child binds half the number of books bound by 1 adult
∴ 1 adult = 2 children
Take work done = 1
∴ (20 adults + 16 children) x 10 days x 1 = (8 adults + 12 children) x ? days x 1

Remember - Convert either all adults to children or all children to adults.

∴ 56 children x 10 days x 1 = 28 children x ? days x 1
∴ ? = 20 days = they will need these many days

8. 12 pumps of one type pump 300 litres of water when each is running for 18 hours per day. But a set of 16 pumps of other type pump 400 litres of water when each is running for 24 hours per day. How efficient are former type of pumps than latter type?

 a. 7 times more efficient 15
 b. 7 times more efficient 12
 c. 3 times more efficient 4
 d. 4 times more efficient 3

 Answer: d. 4 times more efficient 3

Explanation:

Tip:
Men = M; Days = D; Time/Hours = T; Work = W
M1D1T1W2 = M2D2T2W1
Note that - W2 is on left side and W1 is on right side

Let the former type be E times efficient.
So, 1 former type pump = E x latter type pumps
So 1F = E x L
∴ 12F x 18 hours x 400 = 16L x 24 hours x 300
∴ (12 x E x L) x 18 x 400 = 16 L x 24 x 300 ------------------> Put value of F i.e. 1F
 ∴ E = 4 = these many times more efficient 3

9. 75 employees have been able to finish only one-third of the project in 40 hours. The time committed by the management to complete the project was 90 hours. How many more employees should join the team to complete the project on time?

a. 45
b. 55
c. 100
d. 150

Explanation:

Tip:
Men = M; Days = D; Time/Hours = T; Work = W
M1D1T1W2 = M2D2T2W1
Note that - W2 is on left side and W1 is on right side

 Remaining work = 1 - 1 = 2 3 3
Let number of more employees needed be E
 Thus (75+E) employees complete 2 work in 50 hours. 3
 ∴ 75 employees x 40 hours x 2 = (75 + E) x 50 hours x 1 3 3
∴ E = 45 = these many more employees are needed

10. A tank has water for 72 trees and can last for 54 days for them. If each tree is given 10% less water than 90 trees can get the water for how many days?

a. 24 days
b. 36 days
c. 42 days
d. 48 days