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

Answer: d. 72 days

Explanation:

Let work done by Ram in 1 day =1& by Shyam in 1 day =1
RS
Both complete work in 24 days. So in 1 day, together they complete =1=1+1
24RS
For 20 days both work together, so work done by them = 20 1+1 =5
RS6
Remaining work 1 -5=1 is done by Ram alone in 6 days
66
Work done by Ram in 6 days =1= 61
6R
∴ R = 36 = days needed by Ram to complete the work alone
∴1+1=1
36S24
∴ 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

Answer: a. 20 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. 7times more efficient
15
b. 7times more efficient
12
c. 3times more efficient
4
d. 4times more efficient
3

Answer: d. 4times 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
                                                                                                                                                                                                                                  

Answer: a. 45

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
33
Let number of more employees needed be E
Thus (75+E) employees complete2work in 50 hours.
3
∴ 75 employees x 40 hours x2= (75 + E) x 50 hours x1
33
∴ 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
                                                                                                                                                                                                                                  

Answer: d. 48 days

Explanation:

Let each tree take T amount of water every day.
So 72 trees take 72T water in one day.

With 10% reduction each tree will consume90Tamount each day
100
So 90 Trees take 9090Tamount in one day
100
Total water quantity is constant
∴ 72T x 54 = 90 x90Tx D
100
∴ D = 48 days = Number of days 90 trees can use the water.

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