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Two pipes can fill a tank in 15 and 20 hours respectively. The pipes are opened simultaneously and it is found that due to the leakage in the bottom, 17/7 hours extra are taken extra to fill the tank. If the tank is full, in what approximate time would the leak empty it?
- a)27 hrs
- b)32 hrs
- c)36 hrs
- d)39 hrs
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Two pipes can fill a tank in 15 and 20 hours respectively. The pipes a...
Total time taken by both pipes before the leak was developed = 60/7 hours now, leaks is developed which will take T time to empty the tank so, (1/15 +1/20 – 1/T) = 1/11
solve for T, we will get 660/17 hours = 39 hours (approx.)
solve for T, we will get 660/17 hours = 39 hours (approx.)
Most Upvoted Answer
Two pipes can fill a tank in 15 and 20 hours respectively. The pipes a...
Total time taken by both pipes before the leak was developed = 60/7 hours now, leaks is developed which will take T time to empty the tank so, (1/15 +1/20 – 1/T) = 1/11
solve for T, we will get 660/17 hours = 39 hours (approx.)
solve for T, we will get 660/17 hours = 39 hours (approx.)
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Community Answer
Two pipes can fill a tank in 15 and 20 hours respectively. The pipes a...
Given:
- Pipe 1 can fill the tank in 15 hours
- Pipe 2 can fill the tank in 20 hours
- Due to leakage, it takes an extra 17/7 hours to fill the tank
Let's assume the capacity of the tank is 'C'.
Step 1: Calculate the rate of filling
- Pipe 1 can fill 1 tank in 15 hours, so its rate of filling is 1/15 tanks per hour.
- Pipe 2 can fill 1 tank in 20 hours, so its rate of filling is 1/20 tanks per hour.
Step 2: Calculate the combined rate of filling
- The combined rate of filling when both pipes are opened simultaneously is the sum of their individual rates.
- Combined rate = 1/15 + 1/20 = 7/60 tanks per hour.
Step 3: Calculate the time taken to fill the tank with the leakage
- Due to the leakage, it takes an extra 17/7 hours to fill the tank.
- So, the total time taken to fill the tank with the leakage is 17/7 + 15 = 44/7 hours.
Step 4: Calculate the rate of leakage
- The rate of leakage can be calculated by subtracting the combined rate of filling from the rate of filling of the tank.
- Rate of leakage = 1/15 + 1/20 - 7/60 = 1/30 tanks per hour.
Step 5: Calculate the time taken to empty the tank
- Since the rate of leakage is 1/30 tanks per hour, the time taken to empty the tank is the reciprocal of the rate of leakage.
- Time taken to empty the tank = 1 / (1/30) = 30 hours.
Approximately, the time taken to empty the tank is 30 hours, which is closest to option 'D' (39 hours).
- Pipe 1 can fill the tank in 15 hours
- Pipe 2 can fill the tank in 20 hours
- Due to leakage, it takes an extra 17/7 hours to fill the tank
Let's assume the capacity of the tank is 'C'.
Step 1: Calculate the rate of filling
- Pipe 1 can fill 1 tank in 15 hours, so its rate of filling is 1/15 tanks per hour.
- Pipe 2 can fill 1 tank in 20 hours, so its rate of filling is 1/20 tanks per hour.
Step 2: Calculate the combined rate of filling
- The combined rate of filling when both pipes are opened simultaneously is the sum of their individual rates.
- Combined rate = 1/15 + 1/20 = 7/60 tanks per hour.
Step 3: Calculate the time taken to fill the tank with the leakage
- Due to the leakage, it takes an extra 17/7 hours to fill the tank.
- So, the total time taken to fill the tank with the leakage is 17/7 + 15 = 44/7 hours.
Step 4: Calculate the rate of leakage
- The rate of leakage can be calculated by subtracting the combined rate of filling from the rate of filling of the tank.
- Rate of leakage = 1/15 + 1/20 - 7/60 = 1/30 tanks per hour.
Step 5: Calculate the time taken to empty the tank
- Since the rate of leakage is 1/30 tanks per hour, the time taken to empty the tank is the reciprocal of the rate of leakage.
- Time taken to empty the tank = 1 / (1/30) = 30 hours.
Approximately, the time taken to empty the tank is 30 hours, which is closest to option 'D' (39 hours).
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Two pipes can fill a tank in 15 and 20 hours respectively. The pipes are opened simultaneously and it is found that due to the leakage in the bottom, 17/7 hours extra are taken extra to fill the tank. If the tank is full, in what approximate time would the leak empty it?a)27 hrsb)32 hrsc)36 hrsd)39 hrse)None of theseCorrect answer is option 'D'. Can you explain this answer?
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