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12 taps are fitted in a tank in which some are inlet taps and some are outlet taps. Each inlet tap can fill the tank in 30 hours and each outlet tap can empty the tank in 40 hours. Find the number of outlet taps if the whole tank is filled in 6 hours when all the 12 taps are open.

12 taps are fitted in a tank in which some are inlet taps and some are outlet taps. Each inlet tap can fill the tank in 30 hours and each outlet tap can empty the tank in 40 hours. Find the number of outlet taps if the whole tank is filled in 6 hours when all the 12 taps are open. Correct Answer 4

Given:

Total number of taps = 12

Time taken by each inlet tap to fill the tank = 30 hours

Time taken by each outlet tap to empty the tank = 40 hours

Total time taken to fill the tank = 6 hours

Concept used:

Total work = Time taken × Efficiency

And, Total efficiency = efficiency of inlet taps – efficiency of outlet taps

Calculation:

Let total number of inlet taps be x

Total number of outlet taps be (12 – x)

L.C.M of 30 and 40 = 120 units = Total work

Total time taken to fill the tank = 6 hours

Efficiency of all 12 taps = 120/6 = 20 units

Efficiency of each inlet tap = 120/30 = 4 units

Now, Efficiency of x inlet taps = 4x

Efficiency of each outlet tap = 120/40 = 3 units

Efficiency of (12 - x) outlet taps = (36 - 3x)

So, Total efficiency of 9 taps = efficiency of inlet taps – efficiency of outlet taps

⇒ Total efficiency of 12 taps = 4x – (36 – 3x)

So, 4x – (36 – 3x) = 20

⇒ 7x – 36 = 20

⇒ 7x = 56

⇒ x = 8

⇒ Outlet taps = (12 – 8) = 4

∴ The number of outlet taps is 4

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