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

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


Both inlets fill the tank in 48 mins

Inlet one can fill the tank in 2 hrs = 120 mins

inlet two can fill the tank in x mins

1/120 + 1/ x = 1/48
1/x = 1/48 - 1/120 = (5-2)/240 = 3/240 = 1/80

Inlet two can fill the tank in 80 mins

If both inlets opened for 120 mins then
Inlet one will fill full tank capacity
Inlet two will fill 1.5 times capacity of the tank. ---(1)

In every minute inlet two adds 50 cubic meters more than inlet one
In 120 mins inlet two adds 50*120 = 6000 cubic meters more than inlet one.---(2)

From (1) and (2)

Half the capacity of tank is 6000 cubic meters

The capacity of the tank is 12000 cubic meters

Ans d
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Re: With both inlets open, a water tank will be filled with water in 48 [#permalink]
:-D Thankzzz gopu106 VeritasPrepKarishma....... 2 kudos given to both of you
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Re: With both inlets open, a water tank will be filled with water in 48 [#permalink]
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.

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

(C/240) cubic meters/minute * 1 minute = 50 cubic meters

C = 240*50 = 12000 cubic meters
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Re: With both inlets open, a water tank will be filled with water in 48 [#permalink]
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.

(C/240) cubic meters/minute * 1 minute = 50 cubic meters

C = 240*50 = 12000 cubic meters


Thank you very much. As you pointed out C should have been used throughout .
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Re: With both inlets open, a water tank will be filled with water in 48 [#permalink]
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.

(100 + 150) * 48 = 12 000
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Re: With both inlets open, a water tank will be filled with water in 48 [#permalink]
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
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Re: With both inlets open, a water tank will be filled with water in 48 [#permalink]
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First fills in 120 minutes

Together in 48 minutes, then second one fills in 80 minutes. ( 1/120 + 1/second one= 1/48 )

Let first fills x cubic meter per second then second fills (x+50) cubic meter per second

Tank capacity for first = Tank capacity for second
120 * x = 80 * (x + 50)

Solve x =100, i.e first fills at 100 and second at 150 cubic meter per minute

So tank capacity = 120 * 100 or 80*150 = 12,000
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Re: With both inlets open, a water tank will be filled with water in 48 [#permalink]
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
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With both inlets open, a water tank will be filled with water in 48 [#permalink]
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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. 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?

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

Answer: Option D

Please check the video for the step-by-step solution.

GMATinsight's Solution


 
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Re: With both inlets open, a water tank will be filled with water in 48 [#permalink]
Rate for the first pump --> A: tank/2[hs] -->A: tank/120[min]
For the second pump, we know that it has a capacity of more 50cbm per minute than the first pump, so it will complete in the same 2hs the same tank plus that extra volume. So in one hour, the second pump will do 50[cbm/min]*60[min] more than the first pump, in two hours will be the double
Rate for the second pump --> B: tank+50[cbm/min]*60*2/120[min]

Both will be like:

(tank/A + (tank+50*60*2)/B) = tank/48
(tank/120 + (tank+50*60*2)/120) = tank/48
(tank/120 + (tank+6000)/120) = tank/48
(tank/5+ (tank+6000)/5) = tank/2
2*(tank + tank+6000) = tank*5
2*(2*tank + 6000) = tank*5
4*tank + 12000) = tank*5
tank = 12000 --> ANS:D
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Re: With both inlets open, a water tank will be filled with water in 48 [#permalink]
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­Classic rate problem with a twist. Convert 50 cubic meters per minute to per hour and then use x as the total capacity of the tank:

­
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