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Pipe A can fill a tank in ‘an’ hours. On account of a leak at the bott

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Pipe A can fill a tank in ‘an’ hours. On account of a leak at the bott  [#permalink]

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New post 22 Jul 2018, 10:15
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Question Stats:

61% (02:19) correct 39% (02:08) wrong based on 36 sessions

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Pipe A can fill a tank in ‘a’ hours. On account of a leak at the bottom of the tank, it takes thrice as long to fill the tank. How long will the leak at the bottom of the tank take to empty a full tank, when pipe A is kept closed?

a) (3a/2)hours

b) (2a/3)hours

c) (4a/3)hours

d) (3a/4)hours

e) (3a/5)hours

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Re: Pipe A can fill a tank in ‘an’ hours. On account of a leak at the bott  [#permalink]

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New post 22 Jul 2018, 10:30
AkshdeepS wrote:
Pipe A can fill a tank in ‘a’ hours. On account of a leak at the bottom of the tank, it takes thrice as long to fill the tank. How long will the leak at the bottom of the tank take to empty a full tank, when pipe A is kept closed?

a) (3/2)hours

b) (2/3)hours

c) (4/3)hours

d) (3/4)hours

e) (3/5)hours


Say the leak can empty the tank in x hours.
Pipe A can fill a tank in ‘a’ hours.

If there is a leak, the tank is filled in 3a hours. So, (the rate of the pipe A) - (the rate of the leak) = (the rate of the filling):

1/a - 1/x = 1/(3a);
1/x = 1/a - 1/(3a) = 2/(3a);
x = 3a/2.

Answer: A.
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Pipe A can fill a tank in ‘an’ hours. On account of a leak at the bott  [#permalink]

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New post 22 Jul 2018, 12:24
AkshdeepS wrote:
Pipe A can fill a tank in ‘a’ hours. On account of a leak at the bottom of the tank, it takes thrice as long to fill the tank. How long will the leak at the bottom of the tank take to empty a full tank, when pipe A is kept closed?

a) (3a/2)hours

b) (2a/3)hours

c) (4a/3)hours

d) (3a/4)hours

e) (3a/5)hours


in 3a hours, tank should have filled 3 times,
but it filled only 1 time
so, in 3a hours, tank effectively drained 3-1=2 times
therefore, it will drain 1 time in 3a/2 hours
3a/2
a
Pipe A can fill a tank in ‘an’ hours. On account of a leak at the bott &nbs [#permalink] 22 Jul 2018, 12:24
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