Question

A tank can be filled with a tap in 10 hours. However it takes 11 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. 50
2. 130
3. 100
4. 110

Answer 1

Correct Answer - Option 4 : 110

Given:

Tap fills the tank in 10 hours.

And with the leak tank fills in 11 hours.

Formula Used:

Efficiency = Total work done / total  time taken

Total work = LCM of time taken

Calculation:

Let the tap be 'A' and leak be 'B'

Now,

Total work = LCM of time taken

⇒ LCM of 10 and 11

As 10 and 11 are co-prime numbers.

⇒ LCM of 10 and 11 = 10 × 11 = 110

Now,

Efficiency of tap_(A) = 110/10 = 11

Efficiency of leak_{(A - B)} = 110/11 = 10

Efficiency	Subject	Time taken	Total work
11	A	10	110
10	A – B	11	110

⇒ Efficiency of A = 11

⇒ Efficiency of A – B = 10

⇒ Efficiency of B = 1

⇒ Efficiency of leak_(B) = 1

⇒ Time taken to empty the tank by leakage = 110/1

∴ Time taken to empty the tank by leakage is 110 hours.