Question

Four men and three women can do a job in 6 days. When 5 men and 6 women work on the same job, the work gets completed in 4 days. How long will 2 women and 3 men take to do the job?

• A. 18
• B. 10
• C. 8.3
• D. 12

Hint:

Convert everything to a woman's daily rate using 2M = 3W, then divide total work by the new team's combined rate.

Answer 1

The Correct Option is C

Working in terms of a woman's daily rate as the base unit keeps the arithmetic simple throughout.

1. From the two given equations, $(4M+3W)\times 6 = (5M+6W)\times 4$ simplifies to $4M = 6W$, so one man does the work of $1.5$ women per day.
2. Rewrite the first team's rate purely in women-units: $4M + 3W = 4(1.5W) + 3W = 9W$ per day, and over 6 days that totals $54W$ units of work.
3. Rewrite the target team's rate: $2W + 3M = 2W + 3(1.5W) = 6.5W$ per day.
4. Days needed $= \frac{54W}{6.5W} = \frac{540}{65} = \frac{108}{13} \approx 8.3$ days.

So the correct answer is option C, 8.3 days.