Question

Pipe A and Pipe B can fill a tank in 3 and 5 hours respectively. While pipe C can empty a tank in 12 hours. If all pipes are opened together then after 2 hours what portion of the tank will be filled?
1. (9/10)^th
2. (2/5)^th
3. (1/7)^th
4. (6/7)^th

Answer 1

Correct Answer - Option 1 : (9/10)^th

Given:

Pipe A can fill a tank = 3 hours

Pipe B can fill a tank = 5 hours

Pipe C can empty a tank = 12 hours

Calculation:

Total capacity of the tank = 60 units (L.C.M of 3, 5 and 12)

Pipe A filled tank in 1 hour = 60/3

⇒ 20 units

Pipe B filled a tank in 1 hour = 60/5

⇒ 12 units

Pipe C empty a tank in 1 hour = 60/12

⇒ 5 units

Tank filled in 1 hour = 20 + 12 - 5

⇒ 27 units

Tank filled in 2 hour = 27 × 2

⇒ 54 units

Portion of tank filled in 2 hours = (54/60)

⇒ (9/10)^th

∴ (9/10)^th of a tank is filled in 2 hours.