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

Step 1: Set up the total work in two ways.
Let one man's one-day work be M and one woman's one-day work be W. Total work \(=(4M+3W)\times6=(5M+6W)\times4\).

Step 2: Solve for the relation between M and W.
\(24M+18W=20M+24W \Rightarrow 4M=6W \Rightarrow 2M=3W\), so \(M=1.5W\).

Step 3: Find the total work in terms of W.
Total work \(=(4M+3W)\times6=(4\times1.5W+3W)\times6=(6W+3W)\times6=9W\times6=54W\).

Step 4: Find the combined rate of 2 women and 3 men.
Rate \(=2W+3M=2W+3\times1.5W=2W+4.5W=6.5W\) per day.

Step 5: Find the number of days.
Days \(=\dfrac{54W}{6.5W}=\dfrac{54}{6.5}\approx8.3\).

Step 6: Final Answer.
They take about 8.3 days, so option C is correct.