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If a pipe can fill the tank within 6hrs. But due to leak it takes 30 min more.Now the tank is full then how much time will it take to empty the tank throught the leak.?
- a)78
- b)56
- c)66
- d)59
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If a pipe can fill the tank within 6hrs. But due to leak it takes 30 m...
Let the capacity of the tank be 6 litre.
Then time to fill this tank is 6 hour ,when there is no leakage .
so in 1 hour it fills 1 litre.
when leakage is there then it takes 6.5 hour to fill 6 litre
so in 1 hour it fills 6/6.5 litre.
Time to vacate will be 1-(6/6.5) = 1/13 litre in 1 hour
time to vacate 1 litre will be 13 hour.
For 6 litre it will be 13*6 =78
Most Upvoted Answer
If a pipe can fill the tank within 6hrs. But due to leak it takes 30 m...
Given information:
- The pipe can fill the tank within 6 hours.
- Due to a leak, it takes an additional 30 minutes to fill the tank completely.
To find:
- The time it will take to empty the tank through the leak.
Approach:
- First, calculate the rate at which the pipe fills the tank.
- Then, calculate the rate at which the leak empties the tank.
- Finally, use the rate of the leak to find the time it will take to empty the tank completely.
Solution:
Step 1: Calculate the rate at which the pipe fills the tank.
- The pipe can fill the tank in 6 hours, so the rate at which it fills the tank is 1/6 of the tank per hour.
- Let's denote this rate as R1.
Step 2: Calculate the rate at which the leak empties the tank.
- In 6 hours, the tank is filled completely.
- But due to the leak, it takes an additional 30 minutes (0.5 hours) to fill the tank.
- So, the effective time taken by the pipe to fill the tank is 6.5 hours.
- The rate at which the pipe fills the tank is 1/6.5 of the tank per hour.
- Let's denote this rate as R2.
Step 3: Calculate the time it will take to empty the tank through the leak.
- The rate at which the leak empties the tank is the difference between the rates of filling and emptying.
- Rate of leak = R1 - R2
- Rate of leak = 1/6 - 1/6.5
- Rate of leak = (6.5 - 6) / (6 * 6.5)
- Rate of leak = 0.5 / 39
- Rate of leak = 1/78 of the tank per hour.
- To empty the tank completely, it will take the leak 78 hours.
Therefore, the correct answer is option A) 78.
- The pipe can fill the tank within 6 hours.
- Due to a leak, it takes an additional 30 minutes to fill the tank completely.
To find:
- The time it will take to empty the tank through the leak.
Approach:
- First, calculate the rate at which the pipe fills the tank.
- Then, calculate the rate at which the leak empties the tank.
- Finally, use the rate of the leak to find the time it will take to empty the tank completely.
Solution:
Step 1: Calculate the rate at which the pipe fills the tank.
- The pipe can fill the tank in 6 hours, so the rate at which it fills the tank is 1/6 of the tank per hour.
- Let's denote this rate as R1.
Step 2: Calculate the rate at which the leak empties the tank.
- In 6 hours, the tank is filled completely.
- But due to the leak, it takes an additional 30 minutes (0.5 hours) to fill the tank.
- So, the effective time taken by the pipe to fill the tank is 6.5 hours.
- The rate at which the pipe fills the tank is 1/6.5 of the tank per hour.
- Let's denote this rate as R2.
Step 3: Calculate the time it will take to empty the tank through the leak.
- The rate at which the leak empties the tank is the difference between the rates of filling and emptying.
- Rate of leak = R1 - R2
- Rate of leak = 1/6 - 1/6.5
- Rate of leak = (6.5 - 6) / (6 * 6.5)
- Rate of leak = 0.5 / 39
- Rate of leak = 1/78 of the tank per hour.
- To empty the tank completely, it will take the leak 78 hours.
Therefore, the correct answer is option A) 78.
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Community Answer
If a pipe can fill the tank within 6hrs. But due to leak it takes 30 m...
Let the capacity of the tank be 6 litre.
Then time to fill this tank is 6 hour ,when there is no leakage .
so in 1 hour it fills 1 litre.
when leakage is there then it takes 6.5 hour to fill 6 litre
so in 1 hour it fills 6/6.5 litre.
Time to vacate will be 1-(6/6.5) = 1/13 litre in 1 hour
time to vacate 1 litre will be 13 hour.
For 6 litre it will be 13*6 =78
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