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15 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 60 hours. Find the number of inlet taps if the whole tank is filled in 4 hours when all the 15 taps are open.

15 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 60 hours. Find the number of inlet taps if the whole tank is filled in 4 hours when all the 15 taps are open. Correct Answer 10

Given:

Total number of taps = 15

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

Time taken by each outlet tap to empty the tank = 60 hours

Total time taken to fill the tank = 4 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 (15 – x)

L.C.M of 30 and 60 = 60 units = Total work

Total time taken to fill the tank = 4 hours

Efficiency of all 15 taps = 60/4 = 15 units

Efficiency of each inlet tap = 60/30 = 2 units

Now, Efficiency of x inlet taps = 2x

Efficiency of each outlet tap = 60/60 = 1 units

Efficiency of (15 - x) outlet taps = (15 - x)

So, Total efficiency of 15 taps = efficiency of inlet taps – efficiency of outlet taps

⇒ Total efficiency of 15 taps = 2x – (15 – x)

So, 2x – (15 – x) = 15

⇒ 3x – 15 = 15

⇒ 3x = 30

⇒ x = 10

∴ The number of inlet taps is 10

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