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With both inlets open, a water tank will be filled with water in 48 [#permalink]

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31 Oct 2011, 02:07

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With both inlets open, a water tank will be filled with water in 48 minutes. The first inlet alone would fill the tank in 2 hours. What is the capacity of the tank, in cubic meters, if in every minute the second inlet admits 50 cubic meters of water more than the first?

Re: With both inlets open, a water tank will be filled with water in 48 [#permalink]

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31 Oct 2011, 02:58

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aselfmademan wrote:

With both inlets open, a water tank will be filled with water in 48 minutes. The first inlet alone would fill the tank in 2 hours. If in every minutes the second inlet admits 50 cubic meters of water than the first, what is the capacity of the tank ?

With both inlets open, a water tank will be filled with water in 48 minutes. The first inlet alone would fill the tank in 2 hours. If in every minutes the second inlet admits 50 cubic meters of water than the first, what is the capacity of the tank ?

a)10,500 b)12,000 c)9,000 d)11,750 e)13,000

We know that rates are additive. Rate of work of inlet 1 = (1/2) tank/hour = (1/120) tank/min Rate of work of both together = 1/(48/60) = (5/4) tank/hour

Rate of work of inlet 2 alone = 5/4 - 1/2 = 3/4 tank/hour = 1/80 tank/min

We see that rate of work of inlet 2 is higher. 1/80 - 1/120 = 1/240 tank

This (1/240)th of the tank capacity is given as 50 cubic meters. Total tank capacity = 50*240 = 12000 cubic meters
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Re: With both inlets open, a water tank will be filled with water in 48 [#permalink]

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27 Jun 2014, 09:38

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Re: With both inlets open, a water tank will be filled with water in 48 [#permalink]

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11 Jul 2015, 14:57

Hello from the GMAT Club BumpBot!

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Re: With both inlets open, a water tank will be filled with water in 48 [#permalink]

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23 Jul 2015, 12:46

VeritasPrepKarishma wrote:

aselfmademan wrote:

With both inlets open, a water tank will be filled with water in 48 minutes. The first inlet alone would fill the tank in 2 hours. If in every minutes the second inlet admits 50 cubic meters of water than the first, what is the capacity of the tank ?

a)10,500 b)12,000 c)9,000 d)11,750 e)13,000

We know that rates are additive. Rate of work of inlet 1 = (1/2) tank/hour = (1/120) tank/min Rate of work of both together = 1/(48/60) = (5/4) tank/hour

Rate of work of inlet 2 alone = 5/4 - 1/2 = 3/4 tank/hour = 1/80 tank/min

We see that rate of work of inlet 2 is higher. 1/80 - 1/120 = 1/240 tank

This (1/240)th of the tank capacity is given as 50 cubic meters. Total tank capacity = 50*240 = 12000 cubic meters

Hello Madam,

I have a doubt..... is this equation correct :

Assuming C as capacity A as time taken by inlet 1 to fill the tank B as time taken by inlet 2 to fill the tank.

\((\frac{C}{A}+\frac{C}{B})48=C\).........Is this correct ?? We know that inlet 1 takes 2hr or 120 mins to fill the tank

\((\frac{C}{120}+\frac{C}{B})48=C\) Then

\((\frac{1}{120}+\frac{1}{B})48=1\) B=80

I am taking C in the equation for better understanding and because as the rate is not given purely in terms of time taken , as a safer approach I used C.

Also madam as \(\frac{1}{80}-\frac{1}{120}=\frac{1}{240}\)

Can I say 1/240 is the rate difference between the two inlets and (1/240)1 = 50

i.e here 1/240 is the rate, time = 1 and 50 is work done.

With both inlets open, a water tank will be filled with water in 48 minutes. The first inlet alone would fill the tank in 2 hours. If in every minutes the second inlet admits 50 cubic meters of water than the first, what is the capacity of the tank ?

A. 9,000 B. 10,500 C. 11,750 D. 12,000 E. 13,000

The work Done by Inlet A and B together in 1 min = 1/48

The work Done by Inlet A (First Inlet) in 1 min = 1/120

The work Done by Inlet B (Second Inlet) in 1 min = (1/48)- (1/120) = 3/ 240 = 1/80

DIfference of Work done by B and A = B - A = 50 Cubic meter

i.e. (1/80)- (1/120) = 50 Cubic meter i.e. (1/240) of tank = 50 Cubic meter i.e. Tank = 240*50 = 12000 Cubic Meter

Answer: option D
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Assuming C as capacity A as time taken by inlet 1 to fill the tank B as time taken by inlet 2 to fill the tank.

\((\frac{C}{A}+\frac{C}{B})48=C\).........Is this correct ?? We know that inlet 1 takes 2hr or 120 mins to fill the tank

\((\frac{C}{120}+\frac{C}{B})48=C\) Then

\((\frac{1}{120}+\frac{1}{B})48=1\) B=80

Correct.

Quote:

I am taking C in the equation for better understanding and because as the rate is not given purely in terms of time taken , as a safer approach I used C.

Also madam as \(\frac{1}{80}-\frac{1}{120}=\frac{1}{240}\)

This is correct though you should know how you obtained it. 1/80 is the rate and its units are 1/80 of the tank per minute. Since you are using C for capacity, this could also be written as C/80 cubic meters/minute.

So C/80 - C/120 = C/240 cubic meters/minute

Quote:

Can I say 1/240 is the rate difference between the two inlets and (1/240)1 = 50

i.e here 1/240 is the rate, time = 1 and 50 is work done.

Thanks

1/240 of the tank per minute is the rate difference. In capacity terms, C/240 is the rate difference.

Re: With both inlets open, a water tank will be filled with water in 48 [#permalink]

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24 Jul 2015, 11:40

VeritasPrepKarishma wrote:

anurag356 wrote:

Hello Madam,

I have a doubt..... is this equation correct :

Assuming C as capacity A as time taken by inlet 1 to fill the tank B as time taken by inlet 2 to fill the tank.

\((\frac{C}{A}+\frac{C}{B})48=C\).........Is this correct ?? We know that inlet 1 takes 2hr or 120 mins to fill the tank

\((\frac{C}{120}+\frac{C}{B})48=C\) Then

\((\frac{1}{120}+\frac{1}{B})48=1\) B=80

Correct.

Quote:

I am taking C in the equation for better understanding and because as the rate is not given purely in terms of time taken , as a safer approach I used C.

Also madam as \(\frac{1}{80}-\frac{1}{120}=\frac{1}{240}\)

This is correct though you should know how you obtained it. 1/80 is the rate and its units are 1/80 of the tank per minute. Since you are using C for capacity, this could also be written as C/80 cubic meters/minute.

So C/80 - C/120 = C/240 cubic meters/minute

Quote:

Can I say 1/240 is the rate difference between the two inlets and (1/240)1 = 50

i.e here 1/240 is the rate, time = 1 and 50 is work done.

Thanks

1/240 of the tank per minute is the rate difference. In capacity terms, C/240 is the rate difference.

Re: With both inlets open, a water tank will be filled with water in 48 [#permalink]

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13 Jan 2016, 06:27

pipe 2 takes 80 min to fill the tank, pipe 1 - 120 min - which corresponds to +50% produtivity of pipe 2. we are given that this extra productivity denotes 50 cubic meters per min more than pipe 1 pumps. hence this proportion can be possible only if pipe 1 pumps 100 cm and pipe 2 then pumps 150 cm.

Re: With both inlets open, a water tank will be filled with water in 48 [#permalink]

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10 Feb 2017, 10:42

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: With both inlets open, a water tank will be filled with water in 48 [#permalink]

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10 Feb 2017, 13:31

aselfmademan wrote:

With both inlets open, a water tank will be filled with water in 48 minutes. The first inlet alone would fill the tank in 2 hours. If in every minutes the second inlet admits 50 cubic meters of water than the first, what is the capacity of the tank ?

A. 9,000 B. 10,500 C. 11,750 D. 12,000 E. 13,000

rate of inlet 1=r rate of inlet 2=r+60*50 meters^3 per hour ratio of inlet 1 to inlet 2 rates=(1/2)/(5/4-1/2)➡(1/2)/(3/4) (1/2)/(3/4)=r/(r+3000) r=6000 meters^3 per hour 2 hr*6000=12,000 meters^3 capacity

Re: With both inlets open, a water tank will be filled with water in 48 [#permalink]

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14 Aug 2017, 15:25

I think the wording could have been better...second one inlet 50 more than what? a dinosaur? or a first pipe?

I lost a ton of minutes just to realize what the question was actually asking...

I started with finding out the rate for second one: 1/48 (1st and 2nd rate together) - 1/120 (rate of first one) = 1/80 (rate of second one) 1/80 - 1/120 = 1/240 (difference between second and first, and we know that at this rate, 50m^3 is pouring into the pool). capacity of the tank is then 50 * 240 = 100*120 = 12,000