Question

A tank is filled in $5$ hours by three pipes $A,$ $B$ and $C.$ The pipe $C$ is twice as fast as $B$ and $B$ is twice as fast as $A.$ How much time will pipe $A$ alone take to fill the tank?

• A. $35$ hours
• B. $17$ hours
• C. $8$ hours
• D. $30$ hours

Answer 1

The correct option is A $35$ hours

Suppose pipe $A$ alone takes $x$ hours to fill the tank.
Then, pipes $B$ and $C$ will take $\frac{x}{2}$ and $\frac{x}{4}$ hours respectively to fill the tank.
$A,$ $B$ and $C$ together fill $\frac{1}{5}$ part in an hour.
$\therefore \frac{1}{x}+\frac{2}{x}+\frac{4}{x}=\frac{1}{5}$
$\Rightarrow \frac{7}{x}=\frac{1}{5}$
$\Rightarrow x=35$
Hence, pipe $A$ alone takes $35$ hours to fill the tank.