Question

10 men and 8 women can together complete a work in 5 days. Work done by a woman is equal to half of the work done by a man. In how many days will 4 men and 6 women complete that work?

• A. 12
• B. 10
• C. \(8 \frac{2}{3}\)
• D. \(9 \frac{3}{4}\)

Hint:

Express work rates in terms of one unit and combine accordingly to find total work and required time.

Answer 1

The Correct Option is B

Let work done by 1 man in 1 day = \(m\) units
Then work done by 1 woman in 1 day = \(\frac{m}{2}\) units
Work done by 10 men and 8 women in 1 day:
\[ 10m + 8 \times \frac{m}{2} = 10m + 4m = 14m \] Given they finish work in 5 days, so total work:
\[ 5 \times 14m = 70m \] Now, work done by 4 men and 6 women in 1 day:
\[ 4m + 6 \times \frac{m}{2} = 4m + 3m = 7m \] Days to finish work:
\[ \frac{\text{Total Work}}{\text{Work per day}} = \frac{70m}{7m} = 10 \text{ days} \]