Discussion Forum

Two men undertake to do a piece of work for Rs. 240. One could do it alone in 5 days and the other in 8 days. With the help of a boy and a girl they finished it in 3 days. If the work done by the boy be twice that of the girl, what is the share of the girl ?

Answer:

Explanation:

Let name, two men $=A,B$

One boy + girl $=C$

Amount of work $A$ can do in $1$ day $=\frac{1}{5}$

Amount of work $B$ can do in $1$ day $= \frac{1}{8}$

Amount of work $A+B$ can do in $1$ day $=\frac{1}{5}+\frac{1}{8}$ $=\frac{13}{40}$

Amount of work $A+B+C$ can do $=\frac{1}{3}$

Amount of work $C$ can do in $1$ day $= \frac{1}{3}-\frac{13}{40}$ $=\frac{1}{120}$

Work $A$ can do in $1$ day: Work $B$ can do in $1$ day: Work $C$ can do in $1$ day

$=\frac{1}{5} :\frac{1}{8} :\frac{1}{120}$

From the question, one boy work $=2\times$ Girl

So, C = 2Girl + Girl $=\frac{1}{120}$

$\Leftrightarrow$ Girl's one day work $=\frac{1}{360}$

Amount to be paid to Girl $=240\times\frac{1}{120}$ = Rs.2.