Question

A tank can be filled by two taps A and B in 8 hours and 10 hours respectively. The whole tank can be emptied by the third tap in 12 hours. If all the taps are turned on at the same time, in how much time (in how many hours) will the empty tank be completely filled?
1. 9
2. 10
3. 8
4. 7

Answer 1

Correct Answer - Option 4 : 7

Given:

Tap A fill the tank in 8 hours

Tap B fill the tank in 10 hours

Tap C empty the tank in 12 hours

Concept used:

Time = Work/Efficiency

Calculation:

LCM of 8, 10, 12 = 120

Total capacity of tank = 120 units

Efficiency of Tap A = 120/8 = 15 units

Efficiency of Tap B = 120 /10 = 12 units

Efficiency of Tap C = 120/ 12 = 10 units

Effective of these three tanks together = (15 + 12 – 10) = 17 unit

Time taken to fill the tank when they all opened simultaneously = 120 /17 = 7.0588 ≈ 7 hours

∴ The empty tank be completely filled in 7 hours