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Bunuel
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A tank can be filled by Pipe 1 in 7 hours and by Pipe 2 in 5 hours. 21 Jun 2021, 05:15
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65% (hard)

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66% (03:08) correct 34% (03:21) wrong based on 159 sessions

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A tank can be filled by Pipe 1 in 7 hours and by Pipe 2 in 5 hours. There is a waste pipe which is kept open when Pipe 2 is working; the tank then takes 8 hours 30 minutes to fill. What is the approximate time taken to fill the tank if all the three pipes are working?

(A) 3 hours 20 minutes
(B) 3 hours 50 minutes
(C) 4 hours 15 minutes
(D) 4 hours 50 minutes
(E) 5 hours 30 minutes
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A tank can be filled by Pipe 1 in 7 hours and by Pipe 2 in 5 hours. 03 Jul 2021, 21:57
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Bunuel
A tank can be filled by Pipe 1 in 7 hours and by Pipe 2 in 5 hours. There is a waste pipe which is kept open when Pipe 2 is working; the tank then takes 8 hours 30 minutes to fill. What is the approximate time taken to fill the tank if all the three pipes are working?

(A) 3 hours 20 minutes
(B) 3 hours 50 minutes
(C) 4 hours 15 minutes
(D) 4 hours 50 minutes
(E) 5 hours 30 minutes
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Let us consider the pips A, B and C to avoid confusion.

So rate of A \(= \frac{1}{7}\)

Rate of B \(= \frac{1}{5}\)

Let rate of waste pipe \( = \frac{1}{x}\) , we need to find \(\frac{1}{7} + \frac{1}{5} - \frac{1}{x}\\
\)

Also given when pipe B is working and waste pipe is kept open, time taken to fill is \(8.5\) hrs.

So \(\frac{1}{5} - \frac{1}{x} = \frac{1}{8.5}\)

\(\frac{1}{x} = \frac{7}{85} \)

So when all three are kept open :

\( \frac{1}{7} + \frac{1}{5} - \frac{7}{85} = \frac{1}{t} \)

\( t= \frac{119}{31} = 3 \frac{26}{31}\) \(\approx \) \(3\) hrs \(50\) min

Ans-B

Hope it's clear.
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A tank can be filled by Pipe 1 in 7 hours and by Pipe 2 in 5 hours. 04 Jul 2021, 13:14
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Bunuel
A tank can be filled by Pipe 1 in 7 hours and by Pipe 2 in 5 hours. There is a waste pipe which is kept open when Pipe 2 is working; the tank then takes 8 hours 30 minutes to fill. What is the approximate time taken to fill the tank if all the three pipes are working?

(A) 3 hours 20 minutes
(B) 3 hours 50 minutes
(C) 4 hours 15 minutes
(D) 4 hours 50 minutes
(E) 5 hours 30 minutes
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I would attempt this with reasoning.

Pipe 1 fills in 7 hours. If there were two pipes like 1, they will fill the tank in 3.5 hours (3 hours 30 minute). Since the combination of Pipe 2 & Drain pipe fills at 8.5 hours, I would consider that the answer would have to be just a little bit over 3 hours 30 minutes.

This narrows the answer choices to (B), (C) and may be (D).

Similar logic the other way - If two pipes of the same strength as (pipe 2+ drain pipe) were filling the tank, the tank will be filled in half the time i.e. 4 hours 15 minutes. Since pipe A is faster than this combination, the answer has to be less than 4 hours 15 minutes.

Only (B) remains. I would mark (B) without calculation.
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A tank can be filled by Pipe 1 in 7 hours and by Pipe 2 in 5 hours. 08 Jul 2021, 05:05
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Bunuel
A tank can be filled by Pipe 1 in 7 hours and by Pipe 2 in 5 hours. There is a waste pipe which is kept open when Pipe 2 is working; the tank then takes 8 hours 30 minutes to fill. What is the approximate time taken to fill the tank if all the three pipes are working?

(A) 3 hours 20 minutes
(B) 3 hours 50 minutes
(C) 4 hours 15 minutes
(D) 4 hours 50 minutes
(E) 5 hours 30 minutes
Show more

Solution -

Pipe 1 and Pipe 2 can fill the tank in 7 and 5 hours respectively whereas the Waste Pipe takes 8 hours 30 minutes to fill given that Pipe 2 is working.

Let the Waste Pipe be represented as Pipe 3.

Therefore,
The rate at which Pipe 1 can fill the tank = \(\frac{1}{7}\)

The rate at which Pipe 2 can fill the tank = \(\frac{1}{5}\)

The rate at which Pipe 3 can fill the tank = \(\frac{1}{(Pipe 3)}\)

Since, it is given in the question that when Pipe 2 is working and Pipe 3 is kept open, the time taken to fill is 8.5 hours.
So, we can write, the rate = \(\frac{1}{8.5}\)

Therefore, \(\frac{1}{5}- \frac{1}{(Pipe 3)} = \frac{1}{8.5\\
}\)

So, \(\frac{1}{(Pipe 3)} = \frac{1}{5} - \frac{1}{8.5} = \frac{(17-10)}{85} = \frac{7}{85} \\
\)

When all pipes are kept open, the rate will be = \(\frac{1}{7}+ \frac{1}{5} - \frac{7}{85}= \frac{12}{35} - \frac{7}{85}= \frac{155}{595}= \frac{31}{119}\)

Time = \(\frac{1}{(Rate )}= \frac{119}{31}=3.84 \\
\)

To convert 0.84 hours in minutes, we multiply by 60 = 60 * 0.84 = 50.4 minutes

So, the time is approximately 3 hours 50 minutes.


Answer Choice-B
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A tank can be filled by Pipe 1 in 7 hours and by Pipe 2 in 5 hours. 22 Nov 2023, 19:44
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