If both valves are open simultaneously, they can fill an empty pool in

Question

If both valves are open simultaneously, they can fill an empty pool in 48 minutes. The first valve, when working independently, takes 2 hours to fill the pool. If the second valve releases 50 cubic meters of water more than the first valve every minute, what is the capacity of the pool?

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

M12-10

Bunuel · Accepted Answer

If both valves are open simultaneously, they can fill an empty pool in 48 minutes. The first valve, when working independently, takes 2 hours to fill the pool. If the second valve releases 50 cubic meters of water more than the first valve every minute, what is the capacity of the pool?

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

Let the rate of the first valve be  x  cubic meters per minute. The rate of the second valve will then be  x + 50  cubic meters per minute.
 
Given that both valves together fill the pool in 48 minutes, the capacity of the pool can be calculated as  C = 	ext{time}*	ext{combined rate} = 48 	imes (x + x + 50) = 48(2x + 50) .
 
Since the first valve alone fills the pool in 2 hours (or 120 minutes), the capacity of the pool can also be represented as  C = 	ext{time} *	ext{rate} = 120x .
 
Equating the two expressions for  C , we have  120x = 48(2x + 50) . Solving for  x , we get  x = 100 , which implies  C = 120x = 12,000  cubic meters.

Answer: D

KarishmaB · Answer

Responding to a pm:

With both valves open, the pool will be filled with water in 48 minutes. The first valve alone would fill the pool in 2 hours. If the second valve emits 50 cubic meters of water more than the first every minute, then what is the capacity of the pool?

A. 9000 cubic meters
B. 10500 cubic meters
C. 11750 cubic meters
D. 12000 cubic meters
E. 12500 cubic meters

M12-10

(A) 9000 cubic meters
(B) 10500 cubic meters
(C) 11750 cubic meters
(D) 12000 cubic meters
(E) 12500 cubic meters

Normally, I would do this question  the algebra way  (I wouldn't use ratios here because partial data is in time and partial in work form):

Say, capacity of the pool is x cubic meters. Consider time in minutes.

First valve rate = Work/Time = x/120

Second valve rate = x/120 + 50

Combined rate = x/48

x/48 = x/120 + x/120 + 50

x/48 - x/60 = 50

x/4 - x/5 = 12*50

x = 12*50*20 = 12000

But if I am short on time, I can  take a guess .

Most probably, the rate of work will be an integer .... cubic meters per minute. The additional rate of valve 2 is 50 cubic meters per minute so it is unlikely that rate of valve 1 will be something like 150.38 cubic meters per min. It will most probably be an integer.

Assuming that, I see that only option (D) is divisible by 48. 
(48 has four 2s. 9000 has three 2s, 10500 has two 2s, 11750 has one 2 and 12500 has two 2s)

So most probably answer will be 12000. Let's check.

12000/48 = 250
12000/120 = 100
Valve 1 rate is 100 cubic meters per min. Valve 2 rate is 150 cubic meters per min.
Everything matches. 
Answer (D)

scthakur · Answer

D. 12000 cubic meters.

If both hte valves fill the pool in 48 minutes and valve 1 only fills in 120 minutes then valve 2 alone will fill the pool in (48*120)/(120-48) = 80 minutes.

Now, if valve 1 admits x cubic meter of water per minute then the capacity of pool will be 120x and also 80 (x+50).

or, 120x = 80 (x + 50).
or x = 100.

Hence, the capacity of pool = 120x = 12000 cubic meters.

chetan2u · Answer

Hi,

I would think of this in TWO ways if I had to do this Qs WITHOUT getting into serious calculation..

1) USE of CHOICES, as also explained above-  
Very helpful in many calculations..
Ofcourse here, we believe that the speed, x here, must be integer..
so total = 48(x+x+50)..
 so our answer should be a multiple of 48 or 3*16... 
C and E are not multiple of 3..
A and B are multiples of 3, but not of 16..
D

2) second method..  
 In 48 minutes, the faster valve fills up 48*50=2400 more than 1st...
If both took same time as first,that is same speed, the tank would have been filled in 1 hour..

so in 60 - 48= 12 minutes, both would have filled 2400 cum..
BUT first one alone will fill it up in 12*2 = 24 mins...
 if the first fills up 2400 in 24 mins..
it will fill 100 in 1 min and 12000 in 120 mins or 2 hours..
so Capacity of tank = 12000cum 
D

Confusion · Answer

Simplest answer alert. I did this after test and didn't even realise how I could do it:

4/5(V1 + v2)= 2v1
4 v1 + 4v2 = 10V1
2V2=3V1
2(V2-V1)= V1
We know v2-v1 = 50*60 as I have taken volume for per hour
=> 2(3000)=v1
6000=v1
2V1 = full tank = 12000
Tadaaaa

SoHaaM · Answer

suppose total work is 480 units. first valve does = 480/(2*60) = 4u per minute 
first valve + second valve = 480/480=10u per minute, so second valve does = 10-4=6u 
here (6-4)=2u means 50 cubic meters
so, first valve releases (50/2*4)= 100 cubic meter per second 
so it does in 120 minutes = 100*120=12000 cubic meters
so the capacity is 12000 cubic meter

If both valves are open simultaneously, they can fill an empty pool in

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If both valves are open simultaneously, they can fill an empty pool in

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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Perfect 805 Score Debrief by Julia

My Rewards