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There are 12 taps fitted to a cistern in which some are inlet taps and rest are outlet taps. Each inlet tap can fill the cistern in 18 hours and each outlet tap can empty the cistern in 24 hours. Find the difference between the number of inlet and outlet taps, if all the pipes when opened, 1/4th of cistern gets filled in 3 hours.

There are 12 taps fitted to a cistern in which some are inlet taps and rest are outlet taps. Each inlet tap can fill the cistern in 18 hours and each outlet tap can empty the cistern in 24 hours. Find the difference between the number of inlet and outlet taps, if all the pipes when opened, 1/4th of cistern gets filled in 3 hours. Correct Answer 0

Since 1/4th filled cistern gets full in 3 hours.

⇒ A complete cistern will be filled in 3 × (4/1) = 12 hours

Let there are x inlet taps and (12 – x) outlet taps fitted to the cistern

⇒ x/18 – (12 – x)/24 = 1/12

⇒ x/18 + x/24 = 1/12 + 1/2

⇒ 7x/72 = 7/12

⇒ x = 6

⇒ Number of inlet taps = 6 and number of outlet taps = 6

∴ Difference of number of inlet and outlet taps = 6 – 6 = 0

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