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A tank is normally filled in 6 hours but takes two hours longer to fill because of a leak in the bottom of the tank. If the tank is full the leak will empty it in how many hours?
- a)16 hours
- b)18 hours
- c)17 hours
- d)24 hours
- e)None of the Above
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A tank is normally filled in 6 hours but takes two hours longer to fil...
1/8 - 1/x = 1/10
=> x = 40 hrs
Most Upvoted Answer
A tank is normally filled in 6 hours but takes two hours longer to fil...
Work done by leak in 1 hr=(1/6-1/8)=1/24
Leak will empty the tank in 24 hours
Leak will empty the tank in 24 hours
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A tank is normally filled in 6 hours but takes two hours longer to fil...
Solution:
Let us assume that the leak can empty the tank in x hours.
Then, the tank can be filled in 6 hours without any leak and in 8 hours with the leak.
We can use the formula:
Work = Rate × Time
Let us assume that the capacity of the tank is 1 unit.
When the tank is filled without any leak,
Rate of filling the tank = 1/6 unit/hour
When the tank is filled with the leak,
Rate of filling the tank = 1/8 unit/hour
When the tank is emptied by the leak,
Rate of emptying the tank = 1/x unit/hour
Now, we can use the concept of net work to find the time taken by the leak to empty the tank when it is full.
Net rate of filling the tank = Rate of filling the tank - Rate of emptying the tank
= (1/6 - 1/x) unit/hour
As per the given condition, the net rate of filling the tank is zero when the tank is full and the leak starts emptying it.
So, we can write:
(1/6 - 1/x) = 0
=> 1/x = 1/6
=> x = 6 hours
Therefore, the leak will empty the tank in 6 hours when it is full.
Hence, option D (24 hours) is incorrect.
Correct answer: option E (None of the Above).
Let us assume that the leak can empty the tank in x hours.
Then, the tank can be filled in 6 hours without any leak and in 8 hours with the leak.
We can use the formula:
Work = Rate × Time
Let us assume that the capacity of the tank is 1 unit.
When the tank is filled without any leak,
Rate of filling the tank = 1/6 unit/hour
When the tank is filled with the leak,
Rate of filling the tank = 1/8 unit/hour
When the tank is emptied by the leak,
Rate of emptying the tank = 1/x unit/hour
Now, we can use the concept of net work to find the time taken by the leak to empty the tank when it is full.
Net rate of filling the tank = Rate of filling the tank - Rate of emptying the tank
= (1/6 - 1/x) unit/hour
As per the given condition, the net rate of filling the tank is zero when the tank is full and the leak starts emptying it.
So, we can write:
(1/6 - 1/x) = 0
=> 1/x = 1/6
=> x = 6 hours
Therefore, the leak will empty the tank in 6 hours when it is full.
Hence, option D (24 hours) is incorrect.
Correct answer: option E (None of the Above).
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