Question

Three men and 5 women together can finish a job in 3 days. Working on the same job 3 women take 5 days more than the time required by 2 men. What is the ratio of efficiency of a man to a woman?

• A. 2 : 1
• B. 3 : 2
• C. 5 : 2
• D. 4 : 1

Answer 1

The correct option is C 5 : 2

Efficiency of 3 men + 5 women = 33.33%
Let required number of days by 2 men = x
$\therefore$ Required number of days by 3 women = x + 5
Now, consider option (c).
Therefore, 3M + 5W = 3M + 2M = 5 men
Therefore, efficiency of a man = 6.66%
Hence, a man needs 15 days to finish the job, working alone.
Again 3M + 5W = 7.5W + 5W = 12.5W
Therefore, efficiency of a woman = 2.66%
Therefore, a woman needs 37.5 days.
Thus, 2 men need 7.5 days to work alone $\because (7.5=\frac{15}{2})$ and 3 women needs 12.5 days to work alone $\because (12.5=\frac{37.5}{3})$
Hence, the difference in number of days = 5 which is same as given in the problem. Hence correct option is (c).