# 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?

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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?

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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.