A tank can be filled by a tap in 9 hours. However, it takes 10 hours t

A tank can be filled by a tap in 9 hours. However, it takes 10 hours to fill the tank due to a leak. The tap is closed when the tank is full. How many hours will the tank take to empty due to leakage?1. 90 hours2. 100 hours3. 110 hours4. 80 hours

Answer» Correct Answer - Option 1 : 90 hours

Given:

Tank filled = 9 hours

Tank + hole filled = 10 hours

Concept used:

Total capacity = LCM

Efficiency of inlet tap always positive and efficiency of outlet tap is always negative

Formula used:

Efficiency = Total capacity/Time

Calculation

Let P be inlet pipe and Q be leakage

Total capacity = LCM of 9, 10 = 90

Tap	Time	Total capacity	Efficiency
P	9 hours	90	90/9 = 10
P + Q	10 hours	90	90/10 = 9

Efficiency of leakage = 10 – 9 = 1

Time taken by leakage to empty the tank = 90/1 = 90 hours.

∴ Time taken by leakage to empty the full tank is 90 hours

Discussion

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