Question

$A$ and $B$ undertake to do a piece of work for $Rs.600$. $A$ alone can do it in $6$ days while $B$ alone can do it in $8$ days. With the help of $C$ they finish it in $3$ days. Find $B$'s share.

Answer 1

Comparing Work per day, we get

$\Rightarrow \frac{W}{6}+\frac{W}{8}+\frac{W}{C}=\frac{W}{3}$

$\Rightarrow \frac{1}{6}+\frac{1}{8}+\frac{1}{C}=\frac{1}{3}$

$\Rightarrow C=24$

Now, Salary is to be divided according to the Proportion of Work

fraction of Work Done By $B$

$\Rightarrow \frac{WorkByB}{TotalWork}=\frac{\frac{W}{8}}{\frac{W}{3}}=\frac{3}{8}$

So, $B$ will get $\frac{3}{8}$ of the Salary$=\frac{3}{8}\ast 600=225$