Question

4 men or 6 women or 15 children can complete a work in 15 days. Find out the time taken by 2 men, 4 women and 5 children together to complete twice the initial amount of work.
1. 10
2. 15
3. 20
4. 25

Answer 1

Correct Answer - Option 3 : 20

Given :

4 men or 6 women or 15 children can complete a work in 15 days 

Concept used :

working efficiency per day × Total days taken by the person = Total work 

Calculations :

Let the total work be 'W' 

Let the working efficiency of man, woman and children will be 'm' , 'w' and 'c' respectively 

According to the question 

4 m × 15 = 6 w × 15 = 15 c × 15 = W

So, W = 60 m = 90 w = 225 c   

Let time taken by 2 men, 4 women and 5 children be 't' days 

(2 m + 4 w + 5 c) × t = 2 W  

(3 w + 4 w + 2w ) × t = 2 × (90 w)      (4 m = 6 w or 2 m = 3 w, 15 c = 6 w or 5 c = 2 w and W = 90 w)     

9 w × t = 180 w 

t = 20 days

∴ 2 men, 4 women and 5 children will take 20 days together to complete the whole work