20 women can complete a work in 15 days. 16 men can complete the same work in 15 days. Find the ratio between the work efficiency of a man to a woman.

Explanation

Solution: Let's solve this step-by-step. Step 1: Calculate the total work If 20 women can complete the work in 15 days, then the total work (in terms of woman-days) is: Total work = 20 women × 15 days = 300 woman-days Similarly, if 16 men can complete the work in 15 days, then the total work (in terms of man-days) is: Total work = 16 men × 15 days = 240 man-days Step 2: Determine the daily work rate of a woman and a man Since 300 woman-days = 240 man-days for the same work, we can set up the following relationship: 20 women × 15 days = 16 men × 15 days This simplifies to: 20 women = 16 men Dividing both sides by 4, we get: 5 women = 4 men Step 3: Find the efficiency ratio of a man to a woman Now, we know that 5 women have the same work capacity as 4 men. This means the efficiency of 1 man is equal to the efficiency of (5/4) women. Therefore, the ratio of the efficiency of a man to a woman is: 5:4 Answer: The ratio between the work efficiency of a man to a woman is 5:4.