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Due to hole at the bottom of the tank, a tap takes 2 more minutes to c
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03 Dec 2020, 01:15
03 Dec 2020, 01:15
4
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Difficulty:
75%
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Question Stats:
54% (02:28) correct
46%
(02:31)
wrong
based on 82
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Due to hole at the bottom of the tank, a tap takes 2 more minutes to completely fill the tank. Due to leakage of water through this hole, a bucket filled completely with water gets emptied in 4 minutes. In how much time can the tap fill the tank, if there was no hole at the bottom at the tank?
A. 8 min
B. 6 min
C. 4 min
D. 3 min
E. 2 min
A. 8 min
B. 6 min
C. 4 min
D. 3 min
E. 2 min
Re: Due to hole at the bottom of the tank, a tap takes 2 more minutes to c
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04 Dec 2020, 22:11
04 Dec 2020, 22:11
Expert Reply
Bunuel wrote:
Due to hole at the bottom of the tank, a tap takes 2 more minutes to completely fill the tank. Due to leakage of water through this hole, a bucket filled completely with water gets emptied in 4 minutes. In how much time can the tap fill the tank, if there was no hole at the bottom at the tank?
A. 8 min
B. 6 min
C. 4 min
D. 3 min
E. 2 min
A. 8 min
B. 6 min
C. 4 min
D. 3 min
E. 2 min
Logically the bucket should get filled in less than 4minutes, the time it takes the hole to empty the bucket, as otherwise the bucket will never get filled. Only D and E left.
Let the tap fill the bucket in a minutes and with hole, therefore, it will take a+2 minutes.
Therefore the one minute work of the hole =\(\frac{1}{a}-\frac{1}{a+2}=\frac{2}{a(a+2)}\).
But it is given that the bucket empties in 4 minutes, so one minut work of hole =1/4
\(\frac{2}{a^2+2a}=\frac{1}{4}\)
\(a^2+2a=4...........a^2+2a-8=0\)
\((a+4)(a-2)=0\)
Thus a can be -4 or 2. But time cannot be negative, so time taken is 2 minutes
E
Re: Due to hole at the bottom of the tank, a tap takes 2 more minutes to c
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12 Dec 2020, 07:49
12 Dec 2020, 07:49
2
Kudos
Bunuel wrote:
Due to hole at the bottom of the tank, a tap takes 2 more minutes to completely fill the tank. Due to leakage of water through this hole, a bucket filled completely with water gets emptied in 4 minutes. In how much time can the tap fill the tank, if there was no hole at the bottom at the tank?
A. 8 min
B. 6 min
C. 4 min
D. 3 min
E. 2 min
A. 8 min
B. 6 min
C. 4 min
D. 3 min
E. 2 min
Bunuel small typo in source maybe,
Both the vessels in the question should be same, either both should be bucket or both should be tank. Assuming both vessels are same , the question becomes understandable.
The bucket without hole gets filled in \(x\) minutes
The bucket with hole gets filled in \(x+2 \) minutes
The hole empties the whole bucket in 4 minutes.
hence we can form an equation \(\frac{1}{x}-\frac{1}{4}=\frac{1}{x+2}\)
\(x^2+2x-8=0\)
\((x+4)(x-2)=0\)
\(x=2\)
hence the bucket without hole get filled in 2 minutes
Ans-E
Hope it's clear.
