Two Pipes Together Can Fill a Tank In 35 Minutes GMAT Problem Solving

Question: Two pipes together can fill a tank in 35 minutes. The larger pipe alone can fill the tank in 24 minutes less time than the smaller pipe. How long does each pipe take to fill the tank alone?

1. 30 minutes and 54 minutes
2. 40 minutes and 64 minutes
3. 50 minutes and 74 minutes
4. 60 minutes and 84 minutes
5. 70 minutes and 94 minutes

“Two pipes together can fill a tank in 35 minutes.”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “Official Guide for GMAT Reviews”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:

Approach Solution 1:

Assume that a smaller pipe fills the tank in P minutes.
Then, in P - 24 minutes, the larger pipe fills the tank.
Tank filled in 1 minute using a smaller pipe equals 1/P
Tank filled by larger pipe in 1 minute equals 1. (P - 24)
Tank filled in 1 minute by both pipes working together equals 1/P + 1/ (P - 24)
Tank can be filled in 35 minutes using both pipes.
=> 1 minute to fill the tank equals 1/35
=> 1/P + 1/(P - 24) = 1/35
=> 35 ( P - 24 + P) = P(P - 24)
=> 70P - 35 * 24 = P² - 24P
=> P² - 94P + 35 * 24 = 0
=> P² - 84P - 10P + 35 * 24 = 0
=> P (P - 84) - 10(P - 84) = 0
=> (P - 10)(P-84) = 0
=> P = 10 or 84
It is impossible for a larger pipe to fill the tank in P - 24 minutes (10 - 24 = -14).
Thus, the smaller pipe filled the tank in 84 minutes.
Larger pipe filled the tank in 84-24 = 60 minutes.
The answer  60 minutes and 84 minutes

Correct Answer: D

Approach Solution 2: 

There is another approach to solve this question which is pretty easy
Actually, one can immediately rule out three of the options. If each pipe took 70 minutes to complete, they would finish in 35 minutes. The pipes in this issue flow at various rates, therefore one must complete in less than 70 minutes, while the other must require more than 70 minutes.
therefore
> A) Eliminate since Both are less than 70 minutes.
> B) Eliminate since Both are less than 70 minutes.
> C) Keep.
> D) Keep.
> E) Eliminate since Both are greater than or equal to 70 minutes
Testing C and D will now be completed more quickly. If you specify to C that the tank holds 300 litres, then
Pipe A: 50 minutes have passed. Rate = 300/50 = 6.
Pipe B: 60 minutes total time. Rate = 300/60 = 5.
Combined rate for pipes A and B is 11. 11 x 35 equals 385 litres in total. No, it should add up to 300.
We already know the response must be D at this point since C is wrong. We may choose it.
The answer is 60 minutes and 84 minutes

Correct Answer: D

Approach Solution 3:

Let larger pipe can fill the tank in x min and smaller one in y min.

so, y is 24 excess than x

so, x+24=y …….(1)

one pipe in x min fills full (1) part, the pipe in 1 min fills 1/x part, the pipe in 35 min fills 35/x part of the tank .

similarly other pipe in 35 min fills 35/y part of the tank .

in 35 min two pipes together fills the tank full

so, (35/x)+(35/y) =1

or, 35(x+y)=xy

subtituting y=24+x from (1)

we have , 35(x+24+x)=x(24+x)

70x+840=24x+x^2

or, x^2–46x - 840= 0

or, x^2–60x+14x-840=0

or, x(x-60)+14(x-60)=0

or, (x+14)((x-60)=0

or, x=-14, 60

negative value of x not possible

so x=60 min

y= 24+x=60+24=84 min

individually each pipe can fill the tank in 60 min or 84 min.

Correct Answer: D

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