Question

A cistern has a leak at 7 / 12^th height of tank. Pipe can fill the cistern in 30 hours, while if the leak was at bottom, it can empty the cistern in 36 hours. The time (in hours) to fill the cistern is?
1. 87.5
2. 92.5
3. 90
4. 86.5
5. None of these

Answer 1

Correct Answer - Option 2 : 92.5

Given:-

Time for pipe to fill the cistern = 30 hours

Time for leak to empty the tank = 36 hours

Concept used:-

Considering capacity of tank equal to LCM of filling and emptying pipes/leaks.

Calculation:-

Capacity of tank = LCM of (30 and 36) = 360 units

Work done by pipe in 1 hour = 360 / 30 = 12 units.

Work done by leak in 1 hour = 360 / 36 = 10 units.

Leak will only become active when cistern is 7 / 12 filled.

Time required to fill after cistern below leak = 7 / 12 × 360 / 12 = 210 / 12 = 35 / 2 hours

Time required above leak = 5 / 12 × 360 / (12 – 10) = 75 hours

Total time = 75 + 17.5 = 92.5 hours.