Question

If 5 men or 9 women can finish a piece of work in 19 days, 3 men and 6 women can do the same work in how many days?

• A. 12 days
• B. 13 days
• C. 14 days
• D. 15 days

Hint:

When solving work problems, break the task into individual contributions by each worker type (men, women, etc.), then combine their efforts.

Answer 1

The Correct Option is D

Let the work done by 1 man in 1 day be \( \frac{1}{5 \times 19} = \frac{1}{95} \), and the work done by 1 woman in 1 day be \( \frac{1}{9 \times 19} = \frac{1}{171} \). Now, for 3 men and 6 women: \[ \text{Work done by 3 men} = 3 \times \frac{1}{95} = \frac{3}{95} \] \[ \text{Work done by 6 women} = 6 \times \frac{1}{171} = \frac{6}{171} \] Thus, total work done per day is: \[ \frac{3}{95} + \frac{6}{171} = \frac{9}{285} + \frac{6}{171} = \frac{15}{285} = \frac{1}{19} \] Thus, 3 men and 6 women can complete the work in 15 days.