Discussion
30 women can do a certain work in 24 days. 24 men can complete the same work in 21 days. What is the ratio between the capacity of a man and a woman, respectively?
Answer: A
The ratio is 10:7.
The work equals 30 × 24 = 720 woman-days and also 24 × 21 = 504 man-days. So 720 woman-days equal 504 man-days, which means one man does as much as 720/504 = 10/7 women.
\[ \text{man : woman}=\frac{10}{7} \]
7:10 is the inverse and 3:5 and 5:3 do not match the numbers.
You can check the answer by computing the work of one man and one woman in a day. One woman does 1/720 of the work per day and one man does 1/504. The ratio man to woman is (1/504) : (1/720), which equals 720 : 504, and dividing by 72 gives 10 : 7.
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