Multiple choice

If 17 women and 24 men can do a piece of work in 5 days and 12 women and 23 men can do it in 6 days, then which one of the following is correct?

  1. Efficiency of 13 women = Efficiency of 18 men

  2. Efficiency of 11 women = Efficiency of 16 men

  3. Efficiency of 13 women = Efficiency of 17 men

  4. Efficiency of 11 women = Efficiency of 15 men
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A Correct answer
Explanation

Let W be efficiency of a woman, M be efficiency of a man. (17W + 24M) * 5 = (12W + 23M) * 6. 85W + 120M = 72W + 138M. 13W = 18M.

AI explanation

Assume the total job is 30 units. The daily work equations are 17W + 24M = 6 and 12W + 23M = 5. Multiplying the first equation by 5 and the second by 6 yields 85W + 120M = 30 and 72W + 138M = 30. Subtracting the first from the second gives 13W - 18M = 0. This proves that the efficiency of 13 women is equal to the efficiency of 18 men.

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