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6 men and 5 women can complete a piece of work in 6 days while 12 men and 6 women can complete the same piece of work in 4 days. Find the ratio of work efficiency of a man and a woman? 


1. 2 ∶ 3
2. 1 ∶ 2
3. 4 ∶ 5
4. 2 ∶ 5

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Correct Answer - Option 2 : 1 ∶ 2
Given:

6 men and 5 women can complete a piece of work in 6 days while 12 men and 6 women can complete the same piece of work in 4 days.

Concepts used:

Time = Work/Efficiency

Calculation:

Let work efficiency of 1 man be M and work efficiency of 1 woman be W.

Work = Efficiency × Time

⇒ Total work by 6 men and 5 women = (6M + 5W) × 6 = 36M + 30W

⇒ Total work by 12 men and 6 women = (12M + 6W) × 4 = 48M + 24W 

As total work remains same,

⇒ 36M + 30W = 48M + 24W

⇒ 48M – 36M = 30W – 24W

⇒ 12M = 6W

⇒ M/W = ½

∴ Ratio of work efficiency of 1 man and 1 woman is 1 ∶ 2.

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