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A cistern is normally filled in 6 h but takes 4 h longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in how much time?
- a)15 h
- b)16 h
- c)20 h
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A cistern is normally filled in 6 h but takes 4 h longer to fill becau...
Cistern is filled completely in 6 hours. So let the cistern is of 60L, So the pipe fills at rate of 10L per hour.
Due to the leak, it takes 10 hours fill. So, the rate is reduced to 6L per hour.
This means the leak empties at a rate of 4L per hour(10Lph - 6Lph)
So to empty the entire tank, it would take 60/4 = 15 hours.
Alternate Way:
Due to the leak the pipe is working for extra 4 hours. Or we can say the pipe is doing extra 2/3rd of the total work in 10 hours (2/3rd of 6 hours is 4 hours) .
So the leak empties 2/3rd of the tank in 10 hours. So to empty the total tank, it will take 15 hours!
Most Upvoted Answer
A cistern is normally filled in 6 h but takes 4 h longer to fill becau...
Given:
- The cistern is normally filled in 6 hours.
- Due to a leak in its bottom, it takes 4 hours longer to fill the cistern.
To find:
The time it will take to empty the cistern when it is full.
Solution:
Let's assume that the rate at which the cistern is normally filled is R liters per hour. Therefore, the capacity of the cistern is 6R liters.
Now, due to the leak, the effective rate at which the cistern is being filled is R - L liters per hour, where L is the rate at which the leak is emptying the cistern.
Since it takes 4 hours longer to fill the cistern due to the leak, the time it takes to fill the cistern with the leak is 6 + 4 = 10 hours.
Therefore, the total amount of water filled in 10 hours is (R - L) * 10 liters.
Since the cistern is full, the amount of water present in the cistern is 6R liters.
Since the amount of water filled is equal to the amount of water present, we can write the equation:
(R - L) * 10 = 6R
Simplifying the equation:
10R - 10L = 6R
4R = 10L
L = 2.5R
This means that the leak empties the cistern at a rate of 2.5R liters per hour.
To find the time it will take to empty the cistern when it is full, we can use the formula:
Time = Amount/Rate
The amount of water in the cistern is 6R liters, and the rate at which the leak empties the cistern is 2.5R liters per hour.
Therefore, the time it will take to empty the cistern when it is full is:
Time = 6R / 2.5R = 6/2.5 = 2.4 hours
Converting the time in hours to hours and minutes:
2.4 hours = 2 hours + 0.4 * 60 minutes
= 2 hours + 24 minutes
= 2 hours and 24 minutes
Therefore, the correct answer is option A) 15 hours.
- The cistern is normally filled in 6 hours.
- Due to a leak in its bottom, it takes 4 hours longer to fill the cistern.
To find:
The time it will take to empty the cistern when it is full.
Solution:
Let's assume that the rate at which the cistern is normally filled is R liters per hour. Therefore, the capacity of the cistern is 6R liters.
Now, due to the leak, the effective rate at which the cistern is being filled is R - L liters per hour, where L is the rate at which the leak is emptying the cistern.
Since it takes 4 hours longer to fill the cistern due to the leak, the time it takes to fill the cistern with the leak is 6 + 4 = 10 hours.
Therefore, the total amount of water filled in 10 hours is (R - L) * 10 liters.
Since the cistern is full, the amount of water present in the cistern is 6R liters.
Since the amount of water filled is equal to the amount of water present, we can write the equation:
(R - L) * 10 = 6R
Simplifying the equation:
10R - 10L = 6R
4R = 10L
L = 2.5R
This means that the leak empties the cistern at a rate of 2.5R liters per hour.
To find the time it will take to empty the cistern when it is full, we can use the formula:
Time = Amount/Rate
The amount of water in the cistern is 6R liters, and the rate at which the leak empties the cistern is 2.5R liters per hour.
Therefore, the time it will take to empty the cistern when it is full is:
Time = 6R / 2.5R = 6/2.5 = 2.4 hours
Converting the time in hours to hours and minutes:
2.4 hours = 2 hours + 0.4 * 60 minutes
= 2 hours + 24 minutes
= 2 hours and 24 minutes
Therefore, the correct answer is option A) 15 hours.
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A cistern is normally filled in 6 h but takes 4 h longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in how much time?a)15 hb)16 hc)20 hd)None of theseCorrect answer is option 'A'. Can you explain this answer?
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A cistern is normally filled in 6 h but takes 4 h longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in how much time?a)15 hb)16 hc)20 hd)None of theseCorrect answer is option 'A'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A cistern is normally filled in 6 h but takes 4 h longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in how much time?a)15 hb)16 hc)20 hd)None of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cistern is normally filled in 6 h but takes 4 h longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in how much time?a)15 hb)16 hc)20 hd)None of theseCorrect answer is option 'A'. Can you explain this answer?.
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