Question

Pipe $A$ can fill a tank in $4$ hours and pipe $B$ can fill it in 6 hours. If they are opened at alternate hours and if pipe $A$ is opened first, in how many hours will the tank be filled?

• A. $5$ hours
• B. $5\frac{2}{3}$ hours
• C. $4$ hours
• D. $4\frac{2}{3}$ hours

Answer 1

The correct option is D $4\frac{2}{3}$ hours

Portion filled up in 2 hours $=\frac{1}{4}+\frac{1}{6}=\frac{5}{12}$
In 4 hours, portion full $=2\times \frac{5}{12}=\frac{5}{6}$
Remaining portion $\frac{1}{6}$ is filled by A in $4\times \frac{1}{6}=\frac{2}{3}$ hours
$\therefore$ Total time $=4\frac{2}{3}$ hours