Question

Five men and three women can complete a piece of work in 16 days. Nine men and 10 women can complete it in 8 days. Find out in how much time a man can complete it (in days).

• A. 48
• B. 65
• C. 62
• D. 50

Answer 1

Answer: (B)

Let $x$ and $y$ be the capacities of a man and a woman, respectively.
$5x+3y=\frac{1}{16}$(1)
$9x+8y=\frac{1}{10}$(2)
$\text{ Eq. (1) }\times 8-\text{ Eq. (2) }\times 3$
$13x=\frac{1}{2}-\frac{3}{10}=\frac{10-6}{20}$
$\Rightarrow x=\frac{1}{65}$
$\therefore$ A man can complete the work in 65 days.