Question

If $2$ men and $3$ boys can complete a piece of work in $7$ days but $3$ men and $4$ boys can also complete the same work in 5 days, calculate the radio of their working efficiency.

Answer 1

Suppose a man can complete M work in 1 day, while a boy can complete B work in one day.
then, ratio of their working efficiency $=\frac{M}{B}$
Now, $(2M+3B)\times 7=(3M+4B)\times 5$
$14M+21B=15M+20B$
$21B-20B=15M-14M$
$\therefore M=B$
$\Rightarrow \frac{M}{B}=\frac{1}{1}$
i.e., their working efficiencies are equal.