Question

3 men and 6 women complete a work in 5 days if the efficiency of a man is thrice the efficiency of a woman, then in how many days the man complete the work alone?
1. 25 days 
2. 23 days
3. 30 days
4. 20 days

Answer 1

Correct Answer - Option 1 : 25 days 

Given:

3 men + 6 women complete the work in 5 days 

The efficiency of man (M) = 3 × Efficiency of a woman (W)

Concept used:

If the work complete in n days 

then one day work be 1/n part of total work

Calculation:

Let the total work be 1 unit 

Let the one day work of man be M and woman be W

One day work by 3 men and 6 women = 1/5 

⇒ 3M + 6W = 1/5      ----(1)

According to the question

1M = 3W

⇒ W = (1/3)M 

Substitute in equation (1), we get 

⇒ 3M + (6/3)M = 1/5

⇒ 5M = 1/5

⇒ M = 1/25

One day work of man = 1/25

⇒ Number of days = 25

∴ In 25 days the man completes the work alone.