Question

Three pipes $A,B$ and $C$ can fill a tank in $6$ hours. After working at it together for two hours, $C$ is closed and $A$ and $B$ can fill the remaining part in $7$ hours. The number of hours taken by $C$ alone to fill the tank is :

• A. $10$
• B. $12$
• C. $14$
• D. $16$

Answer 1

The correct option is C $14$

A,B and C fill tank in 6 hours. Then A,B and C one hours work =$\frac{1}{6}$

Part filled in two hours$=\frac{2}{6}$=$\frac{1}{3}$

Then remaining part $=1-\frac{1}{2}=\frac{2}{3}$

A and B 7 hours work $=\frac{2}{3}$

Then A and B one hours work $=\frac{2}{21}$

So C one hours work $=(A+B+C)$ one hours work $-(A+B)$ one hours work$=\frac{1}{6}-\frac{2}{21}=$$\frac{1}{14}$

So calone fill the tank in $14$ hours.