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4 women and 10 children can complete a work in 10 days. Then find in how many days 6 men and 6 women can complete 2 times the previous work if the efficiency ratio of a man, a woman and a child is 3 ∶ 2 ∶ 1. 
1. 10
2. 12
3. 18
4. 24

1 Answer

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Correct Answer - Option 2 : 12

Given : 

4 women and 10 children can complete a work in 10 days.

Concept used :

Total work = work efficiency × Total working time. 

Calculations :

Let the efficiency of a man, a woman and a child be 3x, 2x and x units per day. 

Total efficiency of 4 women and 10 children = 4 × 2x + 10 × x = 18x 

Total work done by 4 women and 10 children = 18x × 10 = 180x units 

Now time required to complete two times of this work by 6 men and 6 women 

Total efficiency of 6 men and 6 women = 6 × 3x + 6 × 2x = 30x

Work to be completed = 2 × 180x = 360x units 

So, 

Time × 30x = 360x 

⇒ Time = 12 days 

∴ Option 2 will be the correct answer. 

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