Twenty women can complete a certain task in sixteen days, while sixteen men can finish the same task in fifteen days. Determine the ratio of the efficiency of a man to that of a woman.

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Accepted Answer

The total work done by 20 women in 16 days is equivalent to $$20 	imes 16$$ woman-days. Therefore, the work completed by one woman in one day is given by:

$$
	ext{One woman's daily work} = \frac{1}{20 	imes 16} = \frac{1}{320}.
$$

Similarly, the total work done by 16 men in 15 days is $$16 	imes 15$$ man-days. Hence, the work completed by one man in one day is:

$$
	ext{One man's daily work} = \frac{1}{16 	imes 15} = \frac{1}{240}.
$$

The ratio of the efficiency of a man to a woman is calculated as the ratio of their daily work:

$$
	ext{Required ratio} = \frac{\frac{1}{240}}{\frac{1}{320}} = \frac{320}{240} = 4:3.
$$

Thus, the efficiency ratio between a man and a woman is **4:3**.

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