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03 Dec 2020, 01:15
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
58% (02:34) correct
42%
(02:27)
wrong
based on 195
sessions
History
Date
Time
Result
Not Attempted Yet
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
04 Dec 2020, 22:11
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Bunuel
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
12 Dec 2020, 07:49
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Bunuel
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.
