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.
$5 x+3 y=\frac{1}{16}$(1)
$9 x+8 y=\frac{1}{10}$(2)
$\text { Eq. (1) } \times 8-\text { Eq. (2) } \times 3$
$ 13 x=\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.