Question

If $12$ men and $16$ boys can do a piece of work in $5$ days and $13$ men and $24$ boys can do it in $4$ days, how long will $7$ men and $10$ boys take to do it

Answer 1

$5(12M+16B)=4(13M+24B)$

$60M+80B=52M+96B$

$8M=16B$

$\therefore M=2B$

Now , $12M+16B$ Can do work in $5$ days

So $12M+8M$ can do work in $5$ days

So $20M$ can do work in $5$ days.

Now, $7M+10B=7M+5M=12M$

Hence, if $20M$ can do work in $5$ days

$12M$ can do work in $\frac{20\times 5}{12}$

$=8.33days$