Tap A can fill a cistern in 8 hours and tap B can empty it in 12 hours

1.	Tap A can fill a cistern in 8 hours and tap B can empty it in 12 hours. How long will it take to fill the cistern if both of them are opened together?
Answer» Number of hours Tap A requires to fill an empty tank : 8 hours Number of hours Tap B requires to empty the full tank : 12 hours Amount of water filled by Tap A in empty tank in one hour: \(\frac{1}{8}\) Amount of water Tap B empties in one hour: \(\frac{1}{12}\) Amount of water filled by Tap A and Tap B together in one hour: \(\frac{1}{8}-\frac{1}{12}=\frac{1}{24}\) ∴ They can fill the tank together in 24 hours.

Tap A can fill a cistern in 8 hours and tap B can empty it in 12 hours. How long will it take to fill the cistern if both of them are opened together?

Answer»

Number of hours Tap A requires to fill an empty tank : 8 hours

Number of hours Tap B requires to empty the full tank : 12 hours

Amount of water filled by Tap A in empty tank in one hour: \(\frac{1}{8}\)

Amount of water Tap B empties in one hour: \(\frac{1}{12}\)

Amount of water filled by Tap A and Tap B together in one hour: \(\frac{1}{8}-\frac{1}{12}=\frac{1}{24}\)

∴ They can fill the tank together in 24 hours.