Pipe P can drain the liquid from a tank in 3/4 the time that

Question

Pipe P can drain the liquid from a tank in 3/4 the time that it takes pipe Q to drain it and in 2/3 the time that it takes pipe R to do it. If all 3 pipes operating simultaneously but independently are used to drain liquid from the tank, then pipe Q drains what portion of the liquid from the tank?

A. 9/29
B. 8/23
C. 3/8
D. 17/29
E. 3/4

is the OA A or D???

Even i got it as A=9/29

A. 9/29
B. 8/23
C. 3/8
D. 17/29
E. 3/4

shobhitb · Accepted Answer

A - 9/29

Plugging numbers

P-6hrs
Q-8hrs
R-9hrs

Together in one hr they can drain = 1/6+1/8+1/9 = 29/72 tank

thus together they can drain tank in 72/29 hrs

in 1 hr q drains 1/8 tank
in 72/29 hrs - 72/29*(1/8) = 9/29

sandeep1756 · Answer

Hi Bunuel,

I got the answer by following steps below:
R : P : Q
2 : 3
 4 : 3
combined ratios can be obtained as: 8:12:9
So Q's part is 9/29 of total

Is this the correct way of solving?

XxxyyY · Answer

You got it, Thanks. Apreciate your explanation.

Cheers

faamir · Answer

Suppose Q can drain in 1 hr. So, rQ = 1/1 = 1
So, rP = 1/  = 4/3
Also, rP = rR/(2/3) => 4/3 = rR/(2/3) => rR = 8/9

Let H is the time it takes to drain by running all 3 pipes simultaneously
So combined rate = rC = 1/H = 1 + 4/3 + 8/9 = 29/9 = 1/(9/29)

Thus running simultaneously, Pipe Q will drain 9/29 of the liquid.

Thus answer = A.

Bunuel · Answer

Yes. That's correct.

kzivrev · Answer

I'm doubting if the ratios are correct. trying to figure out how the ratios are seted up, the problem says " P can drain the liquid from a tank in 3/4 the time that it takes pipe Q to drain it and in 2/3 the time that it takes pipe R to do it." or P=(3/4)xQ => P:Q = 3:4 not 4:3 as stated above in red. same thing for the other ratio P=(2/3)xR => P:R = 2:3 
now if we even out P to be 6 ( for 2 and 3) we get P:Q:R = 6:8:9 and Q part will be 8/(8+6+9) = 8/23 which is not correct answer.
Am I missing something or what is wrong here, what do you think  Bunuel  and  sandeep1756

EgmatQuantExpert · Answer

Hi kzivrev , The question gives us the ratio of time taken by Pipes P, Q and R to do a particular work i.e. draining the tank. We know from the time work equation that Work = Rate * Time . So rate is inversely proportional to the time taken . So if the time taken are in the ratio of 2:1 the rates will be in the ratio of 1:2. For example if John can make 6 sandwiches in an hour and Mike can make 6 sandwiches in half an hour the ratio of time taken by John and Mike is 2:1 and hence the ratio of their rates would be 1:2 i.e Mike can make sandwiches twice as fast as John. Coming back to the question, if all the 3 pipes work simultaneously, they would be working for the same amount of time.Hence to find the proportion of work done by pipe Q we need to find the ratios of rates of pipes P, Q and R . Since the ratio of time taken by pipes P & Q to do a particular work is 3:4, the ratio of their rates would be 4:3. On the same lines, if the ratio of time taken by pipes P & R to do a particular work is 2:3, the ratio of their rates would be 3:2. Hence if we assume the rate of pipe P as x , we can write the rate of pipe Q as \frac{3x}{4} and rate of pipe R as \frac{2x}{3} . The proportion of work done by pipe Q can be calculated as rate of pipe Q divided by the total rates of pipe P, Q and R. The sum of the rates of pipes P, Q and R is \frac{29x}{12} . Hence the proportion of work done by pipe Q would be \frac{3x * 12}{4 * 29x} = \frac{9}{29} . Hope its clear

Regards Harsh

ScottTargetTestPrep · Answer

We can let p = the time it takes pipe P to drain the liquid from the tank. Thus, the rate of pipe P = 1/p.

Since pipe P can drain the liquid from the tank in 3/4 the time that it takes pipe Q to drain it, the rate of pipe Q is:

(3/4)(1/p) = 3/(4p)

Since pipe P can drain the liquid from the tank in 2/3 the time that it takes pipe R to do it, the rate of pipe R is:

(2/3)(1/p) = 2/(3p)

Thus, the portion of liquid pipe Q drains is:

/

Multiplying the numerator and denominator by 12p, we have:

9/(12 + 9 + 8)

9/29

Answer: A

gracie · Answer

relative times & rates are:
P: 6/8 & 96/72
Q: 8/8 & 72/72
R: 9/8 & 64/72
combined rate=232/72
portion drained by Q=(72/72)/(232/72)=9/29
A

hellosanthosh2k2 · Answer

P - rate of P, Q - rate of Q, R - rate of R
P = 4/3Q (as P takes 3/4 th time of Q)
P = 3/2R (as P takes 2/3 th time of R) => R = 8/9Q
P : Q : R = 4/3 : 1 : 8/9 = 12 : 9 : 8
Q's portion = 9/(12+9+8) = 9/29

lostnumber · Answer

I was able to solve through until I got to the highlighted portion, is someone able to explain how to go from R= 8/9Q to this three part ratio? Math is hard

GMATinsight · Answer

Answer: Option A Please check the solution as attached. Screenshot 2020-08-05 at 7.37.56 AM.png

KarishmaB · Answer

P takes 3/4th time of Q so its rate is 4/3 of Q. Rate of P : Q = 4 : 3 P takes 2/3rd time taken by R so its rate is 3/2 of R. Rate of P : R = 3 : 2 Combining the two ratios, we get Rate of P:Q:R = 12 : 9 : 8 Hence Q does 9/(12 + 9 + 8) = 9/29 of the work Answer (A) Here is a video discussion on work-rate using ratios: https://youtu.be/88NFTttkJmA and check out these posts: https://anaprep.com/arithmetic-applying ... -concepts/ https://anaprep.com/arithmetic-work-rat ... s-and-all/ https://anaprep.com/arithmetic-avoiding ... work-rate/

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Pipe P can drain the liquid from a tank in 3/4 the time that

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