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A water tank normally takes 6 hours to be filled by a tap but because

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Bunuel
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A water tank normally takes 6 hours to be filled by a tap but because [#permalink] New post   08 Feb 2021, 04:15
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A water tank normally takes 6 hours to be filled by a tap but because of the leak, it takes another 1 hour. In how many hours will the leak empty a full water tank ?

(A) 42 hours
(B) 39 hours
(C) 36 hours
(D) 31.5 hours
(E) 30 hours
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A
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Re: A water tank normally takes 6 hours to be filled by a tap but because [#permalink] New post   14 Feb 2021, 05:00
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The tank normally takes 6hrs to fill but due to leak it takes 7 hrs to fill.
Suppose we have a 42cc tank.
Rate at which it would normally fill = 42/6 = 7cc/h
Rate at which it would normally with the leak = 42/7 = 6cc/h

So due to leak we have a decrease of 1cc/h.
At this rate time that the leak would take to empty this 42cc tank = 42cc / 1cc/hr = 42 hrs

Ans: A
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sthahvi
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Re: A water tank normally takes 6 hours to be filled by a tap but because [#permalink] New post   07 Apr 2021, 19:36
can someone solve this ?
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harvar
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A water tank normally takes 6 hours to be filled by a tap but because [#permalink] New post   07 Apr 2021, 20:33
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sthahvi

Normal Rate to fill one tank = 1/6

Lets assume it takes x hrs for the leak to empty the tank; so the rate of leak = 1/x

From the stem, due the leak the new rate is given as :

Normal Rate - Leak rate = 1/7

1/6 - 1/x = 1/7

x-6/6x = 1/7

7x - 42 = 6x

x = 42
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Re: A water tank normally takes 6 hours to be filled by a tap but because [#permalink] New post   07 Apr 2021, 20:50
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Lets say the capacity of the tank is x litres
x litres can be filled in 6 hours
Because of leak x litres can now be fixed in 6 + 1 hours i.e. 7 hours.

Thus rate of tank in 1 hour is x / 7 earlier being x / 6 thus rate of leakage is x / 6 - x / 7 = x / 42

Now x/42 is your rate of leakage. It just translates to x litres of the tank can be emptied in 42 hours. Hence answer A
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Re: A water tank normally takes 6 hours to be filled by a tap but because [#permalink] New post   17 Apr 2021, 22:38
Rate of filling the tank without leak = 1/6
Rate of filling the tank with leak = 1/7

Therefore, the difference of the two = rate of emptying the tank = 1/42

Take reciprocal for total number of days: Ans = 42
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Re: A water tank normally takes 6 hours to be filled by a tap but because [#permalink] New post   04 Mar 2024, 15:24
Hello from the GMAT Club BumpBot!

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Re: A water tank normally takes 6 hours to be filled by a tap but because [#permalink]
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