Question

A tap can fill the cistern in 6 hrs and second one can empty the cistern in 8 hrs. If the cistern is empty, find the time taken by both the taps to fill the tank when opened simultaneously.
1. 20 hrs
2. 14 hrs
3. 10 hrs
4. 24 hrs
5. None of these

Answer 1

Correct Answer - Option 4 : 24 hrs

Given:

The first tap can fill the cistern in 6 hrs

The second tap can empty the tank in 8 hrs

Concept used:

Time ∝ 1/Efficiency

Calculation:

Taking the L.C.M of 6 and 8 

L.C.M of 6 and 8 = 24

⇒ Efficiency of first tap = 24/6 = 4

⇒ Efficiency of second tap = 24/8 = 3

1-hour work when both taps are opened = 4 - 3 = 1

Both taps will fill the tank in 24/1 = 24 hrs

∴ The required time is 24 hours.