WBCS Mains 2020 Official Paper-VI

$A$ and $B$ can do a piece of work in $10$ days, $B$ and $C$ in $12$ days, and $C$ and $A$ in $15$ days. The number of days taken by $A$, $B$, and $C$ working together to finish the work is

Pipe $A$ can fill a tank in $3$ hours and pipe $B$ can fill it in $4$ hours. If they are opened at alternate hours and if pipe $A$ is opened first, in how many hours will the tank be filled?

Six years hence, a man's age will be three times the age of his son and three years ago he was nine times as old as his son. The present age of the man is

$76$ ladies can do a job in $33$ days. Due to some reason, some ladies did not join the work and therefore, it was completed in $44$ days. The number of ladies who did not join the work is

In a joint business, the ratio of the capitals of three friends was $\frac{1}{2}:\frac{1}{3}:\frac{1}{4}$. After $4$ months, the first friend withdrew half of his capital and $8$ months thereafter, $\text{Rs. }2024$ was recorded as their total profit. What was the share of profit of the first friend?