Question

A cistern filled in $20$ hours by three pipes A, B and C. The pipe C is twice as fast as B and B is thrice as fast as A. How much hours will pipe A alone take to fill the tank?

• A. $200$
• B. $400$
• C. $900$
• D. $100$

Answer 1

The correct option is A $200$

Suppose pipe $A$ alone takes $x$ hours to fill the tank.

Then pipes $B$ and $C$ will take $\frac{x}{3}$ and $\frac{x}{6}$ hours respectively to fill the tank.

$\therefore \frac{1}{x}+\frac{3}{x}+\frac{6}{x}=\frac{1}{20}$

$\Rightarrow \frac{10}{x}=\frac{1}{20}$

$\Rightarrow x=200$hours.

$\therefore$ pipe $A$ alone will take $200$hours to fill the tank .