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# A certain water tank has two outlet valves, valve A and valve B. Each

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Joined: 03 Jul 2017
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Location: India
Concentration: Finance, Economics
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A certain water tank has two outlet valves, valve A and valve B. Each  [#permalink]

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Updated on: 03 Dec 2017, 20:50
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85% (hard)

Question Stats:

50% (02:11) correct 50% (02:28) wrong based on 85 sessions

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A certain water tank has two outlet valves, valve A and valve B. Each valve drains water from the tank at a constant rate. If the tank is full and valve B alone is opened, does it take more than two hours to completely drain the tank?

(1) When the tank is full, if valve A alone is opened, it takes 4 hours to completely drain the tank.

(2) When the tank is full, if valve A is opened and valve B is opened an hour later, it takes 4/3 as long to completely drain the tank as it would if both valves had been opened simultaneously from the start.

Originally posted by abansal1805 on 03 Dec 2017, 00:05.
Last edited by Bunuel on 03 Dec 2017, 20:50, edited 1 time in total.
Edited the question.
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Re: A certain water tank has two outlet valves, valve A and valve B. Each  [#permalink]

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03 Dec 2017, 20:48
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2
abansal1805 wrote:
A certain water tank has two outlet valves, valve A and valve B. Each valve drains water from the tank at a constant rate. If the tank is full and valve B alone is opened, does it take more than two hours to completely drain the tank?

(1) When the tank is full, if valve A alone is opened, it takes 4 hours to completely drain the tank.

(2) When the tank is full, if valve A is opened and valve B is opened an hour later, it takes as long to completely drain the tank as it would if both valves had been opened simultaneously from the start.

The question has a typo. It should be it takes 4/3 as long to completely drain the tank

A certain water tank has two outlet valves, valve A and valve B. Each valve drains water from the tank at a constant rate. If the tank is full and valve B alone is opened, does it take more than two hours to completely drain the tank?

(1) When the tank is full, if valve A alone is opened, it takes 4 hours to completely drain the tank. No info on valve B. Not sufficient.

(2) When the tank is full, if valve A is opened and valve B is opened an hour later, it takes 4/3 as long to completely drain the tank as it would if both valves had been opened simultaneously from the start.

Say the rate of valve A is a tank/hour and the rate of valve B is b tank/hour.

In 1 hour valve A would drain (rate)(time) = a*1 = a part of the tank. So, 1 - a part of the tank will be left to drain. To drain 1 - a part of the tank, both A and B will need $$(time) = \frac{(job)}{(rate)} = \frac{(1 - a)}{(a + b)}$$ hours. So, the total time in this case is $$1 +\frac{(1 - a)}{(a + b)}$$ hours.

Next, to drain the full tank from the start, both A and B will need $$(time) = \frac{(job)}{(rate)} = \frac{1}{(a + b)}$$ hours.

We are told that: $$1 + \frac{(1 - a)}{(a + b)} = \frac{4}{3}*\frac{1}{(a + b)}$$.

$$\frac{3(b+1)}{a+b}=\frac{4}{a+b}$$;

From this we can get that $$b = \frac{1}{3}$$ tank/hour. So, the time it would take valve B to drain the tank is 3 hours. Sufficient.

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Re: A certain water tank has two outlet valves, valve A and valve B. Each  [#permalink]

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03 Dec 2017, 21:23
Hi, Can you pls tel how total time was derived ? 1+(1−a)/(a+b) , I got the logic behind (1-a)/(a+b), but not 1 + (1-a)/(a+b)
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Posts: 52343
Re: A certain water tank has two outlet valves, valve A and valve B. Each  [#permalink]

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03 Dec 2017, 22:05
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kunal20 wrote:
Hi, Can you pls tel how total time was derived ? 1+(1−a)/(a+b) , I got the logic behind (1-a)/(a+b), but not 1 + (1-a)/(a+b)

"Valve A is opened and valve B is opened an hour later, ..." So, for an hour valve A drained the tank alone. After B joined together they needed (1−a)/(a+b) hours, hence total of 1 + (1−a)/(a+b) hours.
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Re: A certain water tank has two outlet valves, valve A and valve B. Each  [#permalink]

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03 Dec 2017, 22:08
Bunuel wrote:
kunal20 wrote:
Hi, Can you pls tel how total time was derived ? 1+(1−a)/(a+b) , I got the logic behind (1-a)/(a+b), but not 1 + (1-a)/(a+b)

"Valve A is opened and valve B is opened an hour later, ..." So, for an hour valve A drained the tank alone. After B joined together they needed (1−a)/(a+b) hours, hence total of 1 + (1−a)/(a+b) hours.

Got it. Thanks Bunuel
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Re: A certain water tank has two outlet valves, valve A and valve B. Each  [#permalink]

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03 Dec 2017, 22:34
abansal1805 wrote:
A certain water tank has two outlet valves, valve A and valve B. Each valve drains water from the tank at a constant rate. If the tank is full and valve B alone is opened, does it take more than two hours to completely drain the tank?

(1) When the tank is full, if valve A alone is opened, it takes 4 hours to completely drain the tank.

(2) When the tank is full, if valve A is opened and valve B is opened an hour later, it takes 4/3 as long to completely drain the tank as it would if both valves had been opened simultaneously from the start.

Thankyou Bunuel for noticing the mistake and editing this one. I was pretty confused. Heres how I did this:

Let valve A drains 'a' units per hour, let valve B drains 'b' units per hour, and let the water in tank be total 'a*b' units.
So valve A will take = ab/a = b hours, while valve B will take = ab/b = a hours : to drain water on their own each. We need to know whether a > 2 or not?

(1) valve A alone takes 4 hours or b=4. or total water in tank = 4a units. But this doesnt give the answer to our question. Insufficient.

(2) if both valves are opened simultaneously, units of water drained per hour = (a+b), thus time taken = ab/(a+b)
IF instead first A is opened for 1 hour, 'a' units of water already drained in one hour. Units left in tank = (ab-a) ...now both valves are opened and units being drained per hour = a+b, thus further time now required to drain completely = (ab-a)/(a+b). So total time required in this case = 1 + (ab-a)/(a+b) OR (b+ab)/(a+b)

We are given that this latter time is 4/3 or the former time, so we can write this as:
(b+ab)/(a+b) = 4/3 * ab/(a+b) ... Solving we get: a+1 = 4a/3 Or a=3. So we get that a>2 (or valve B will take more than 2 hours to drain the tank). Sufficient.

Re: A certain water tank has two outlet valves, valve A and valve B. Each &nbs [#permalink] 03 Dec 2017, 22:34
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