If a pipe can fill the tank within 5 (1/2 ) hours but due to leak it takes 30…
2024
If a pipe can fill the tank within 5 (1/2 ) hours but due to leak it takes 30 minutes more . If the tank is full then how much time will it take to empty the tank through the leak ?
- A.
70 hrs
- B.
66 hrs
- C.
60 hrs
- D.
56 hrs
Attempted by 642 students.
Show answer & explanation
Correct answer: B
Key idea: compute rates (fraction of tank per hour) and subtract to find the leak rate.
Step 1: Filling pipe alone fills the tank in 5.5 hours, so its rate = 1/5.5 = 2/11 tank per hour.
Step 2: With the leak, the tank is filled in 30 minutes more = 6 hours, so the net filling rate = 1/6 tank per hour.
Step 3: Leak emptying rate = filling rate - net rate = 2/11 - 1/6 = (12 - 11)/66 = 1/66 tank per hour.
Step 4: Time for the leak alone to empty a full tank = reciprocal of 1/66 = 66 hours.
Answer: 66 hours