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. $5:4$

Answer 1

Answer: (A)

$2:1$

Let $1$ man's $1$ day's work be $x$ and $1$ boy's $1$ day's work be $y$.

Then,

$12x+16y=\frac{1}{5}$ .....(1)

$13x+24y=\frac{1}{4}$ .....(2)

Solving equation (1) and (2), we get,

$x=\frac{1}{100}$ and $y=\frac{1}{200}$

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