Question

Pipe X and Y can fill a tank in 8 hrs and 6 hrs respectively. Pipe R can empty the tank in 12 hrs. All the three pipes are opened simultaneously, and the tank is half full. In how much time the tank will be filled?
1. 4.2 hrs
2. 6 hrs
3. 2.4 hrs
4. 5 hrs
5. None of these

Answer 1

Correct Answer - Option 3 : 2.4 hrs

Given:

Pipe X can fill the tank in 8 hrs

Pipe Y can fill the tank in 6 hrs

Pipe Z can empty the tank in 12 hrs

Concept used:

Let, Pipe A can fill a tank in x hrs

⇒ Pipe A can fill a tank in 1 hr = 1/x

Calculation:

Pipe X can fill the tank in 1 hr = 1/8

Pipe Y can fill the tank in 1 hr = 1/6

Pipe Z can empty the tank in 1 hr = 1/12

According to the question,

⇒ (1/8) + (1/6) - (1/12)

⇒ (3 + 4 - 2)/24

⇒ (5/24)

⇒ Required time = (24/5) × (1/2) = 12/5 = 2.4 hrs

∴ The time in which half of the tank will be filled is 2.4 hrs.