Question

If 12 men and 16 boys can do a piece of work in 5 days; 13 men and 24 boys can do it in 4 days, then the ratio of the daily work done by a man to that of a boy is:

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

Answer 1

The correct option is A

2:1

Let 1 man’s 1 day’s work = x and 1 boy’s 1 day’s work = y

Then, $12x+16y=\frac{1}{5}and13x+24y=\frac{1}{4}$

Solving these two equations, we get : x = $\frac{1}{100}$ and y = $\frac{1}{200}$

$\therefore$ Required ratio = x:y = $\frac{1}{100}:$ $\frac{1}{200}$ = 2:1