Question

$2$ men and $5$ boys together can finish a piece of work in $4$ days, while $3$ men and $6$ boys can finish it in $3$ days. Find the time taken:
i) by one man alone to finish the work
ii) by one boy alone to finish the work.

• A. $18$ days and $36$ days
• B. $22$ days and $18$ days
• C. $11$ days and $13$ days
• D. $17$ days and $16$ days

Answer 1

The correct option is A $18$ days and $36$ days

Let the amount of work done by a Man alone in a day be $M$ and by a Boy alone be $B$
Given, $2$ men and $5$ boys together can finish a piece of work in $4$ days
Amount of work they can do in one day $2M+5B$ $=\frac{1}{4}$ -- (1)
Similarly, $3M+6B=\frac{1}{3}$ --- (2)
Solving equations $\left(1\right)$ and $\left(2\right)$, we get $B=\frac{1}{36}$

Substituting $B$ in equation $\left(2\right)$, we get $M=\frac{1}{18}$
Hence, one man alone will take $18$ days to do the work and one boy will take $36$ days.