Question

Two inlet pipes can fill a cistern in 10 and 12 hours respectively and an outlet pipe can empty 80 gallons of water hour. All the three pipes working together can fill the empty cistern in 20 hours. What is the capacity (in gallons) of the tank?

• A. 360
• B. 300
• C. 600
• D. 900

Answer 1

The correct option is C 600

If the outlet pipe alone empty the cistern in $=x$ hours, then.

$\frac{1}{10}+\frac{1}{12}-\frac{1}{x}=\frac{1}{20}$

So $\frac{1}{x}=\frac{1}{10}+\frac{1}{12}-\frac{1}{20}$

$\frac{1}{x}=\frac{6+5–3}{60}=\frac{8}{60}=\frac{2}{15}$

Therefore the outlet pipe can empty the cistern in $=\frac{15}{2}=7.5$ hours.

In $1$ hour the outlet pipe can empty $=80$ Gallons.

So in $7.5$ hours it can empty$=7.5\times 80=600$ Gallons.

Therefore the capacity of the cistern $=600$ Gallons.