Discussion Forum

$1$ man, $3$ women and $4$ boys can do a piece of work in $96$ hours, $2$ men and $8$ boys can do it in $80$ hours, $2$ men and $3$ women can do it in $120$ hours. $5$ men and $12$ boys can do it in :

Answer:

Explanation:

Let $1$ man's hour's work $=x$, $1$ woman's $1$ hour's work $=y$ and $1$ boy's $1$ hour's work $=z$.

Then, $x+3y+4z=\frac{1}{96}$ ---(1)

$2x+8z=\frac{1}{80}$ ---(2)

$2x+3y=\frac{1}{120}$ ---(3)

Adding (2) and (3) and subtracting (1) from it, we get : $3x+4z=\frac{1}{96}$---(4)

From (2) and (4), we get $x=\frac{1}{480}$.

Substituting, we get : $y=\frac{1}{720}$, $z=\frac{1}{960}$.

($5$ men + $12$ boy's) $1$ hour's work $=\left(\frac{5}{480}+\frac{12}{960}\right)$ $=\left(\frac{1}{96}+\frac{1}{80}\right)$ $=\frac{11}{480}$.

$\therefore$ $5$ men and $12$ boys can do the work in $\frac{480}{11}$

i.e, $43\frac{7}{11}$ hours.