A cistern has a hole in the bottom through which the water is leaking. A tap can fill the cistern in 8 hours and the hole in the bottom can empty the fully filled cistern in 12 hours. If both the tap and the hole are open, then what will be the time taken to completely fill the empty cistern?​

Correct option is D

Given:

Tap can fill the cistern in 8 hours

Hole can empty the full cistern in 12 hours

Both are open simultaneously

Required: Time to fill the cistern completely

Formula Used: 

Total Capacity = work rate $$\times$$ time

Work per hour = Fill rate – Leak rate

Solution:

Let total capacity of cistern =LCM of 8 and 12 = 24 units

Then:

Tap fills 24 ÷ 8 = 3 units/hour

Hole leaks 24 ÷ 12 = 2 units/hour

Net work = 3 – 2 = 1 unit/hour

Time = $$\frac{24}{1}$$​ = 24 hours