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Doctors Medicines MCQs Q&A

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1 Answers

Option 2 : 3

Given:

Total number of taps = 4

Time taken by each inlet tap to fill the tank = 24 hours

Time taken by each outlet tap to empty the tank = 8 hours

Total time taken to empty the tank = 3 hours

Concept used:

Total work = Time taken × Efficiency

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

Calculation:

Let total number of inlet taps be x

Total number of outlet taps be (4 – x)

L.C.M of 24 and 8 = 24 units = Total work

Total time taken to empty the tank = 3 hours

Efficiency of all 4 taps = 24/3 = -8 units

Here, negative sign in efficiency shows tank is emptying

Efficiency of each inlet tap = 24/24 = 1 units

Now, Efficiency of x inlet taps = x

Efficiency of each outlet tap = 24/8 = 3 units

Efficiency of (4 - x) outlet taps = (12 - 3x)

So, Total efficiency of 4 taps = efficiency of inlet taps – efficiency of outlet taps

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

So, x – (12 – 3x) = -8

⇒ 4x – 12 = -8

⇒ 4x = 4

⇒ x = 1

⇒ Outlet taps = (4 – 1) = 3

∴ The number of outlet taps is 3

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