Two Pipes can Fill A Tank in 20 and 24 Minutes Respectively and A Wast GMAT Problem Solving

Question: Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank in gallons is

1. 100
2. 110
3. 120
4. 140
5. 150

Answer:
Approach Solution (1):
Let us take the LCM of 20, 24, and 15 = 120
So assume we have 120 units of work to be done
Time taken by pipe A = 20 minutes
Therefore work done in 1 minute =\(\frac{120}{20}=6\)
Time taken by Pipe B = 24 minutes
Therefore work done in 1 minutes =\(\frac{120}{24}=5\)
Let time taken by pipe C (outlet) = x minutes.
Therefore work done in 1 minute =\(\frac{120}{x}\)
Total time to fill = 15 minutes
Therefore work done in 1 minute =\(\frac{120}{15}=8\)
Therefore, 6 + 5 -\(\frac{120}{x}\)= 8
\(\frac{120}{x}\)= 11 – 8 = 3
x = 40
In 1 minute the outlet pipe empties 3 gallons
Therefore in 40 minutes = 40 * 3 = 120 gallons
Correct option: C

Approach Solution (2):
S1: Two pipes can fill a tank in 20 and 24 minutes
So, together they can fill a tank in:
\(\frac{1}{20}+\frac{1}{24}=\frac{11}{120}\)
i.e. To fill N gallons of tank – Two pipes can fill in \(\frac{120}{11}\) minutes --- (1)
S2: Since, the tank was filled in 15 minutes; amount of water wasted will get added to original capacity of tank
Amount of water wasted – 15 minutes * 3 (gallons/minute) = 45 gallons
So to fill N + 45 gallons of tank – two pipes can fill in 15 minutes --- (2)
Comparing (1) and (2)
\(\frac{N}{N+45}=\frac{120}{11*15}\)
11N = 8N + 45 * 8
3N = 45 * 8
N = 15 * 8
N = 120
Correct option: C

Approach Solution (3):
According to given question:
Two pipes can fill tank = 20 and 24 minutes
A waste pipe can empty = 3 gallon/min
Three pipes working = 15 minutes
So, according to given question:
Work done by the waste pipe in 1 minute
\(=\frac{1}{15}-(\frac{1}{20}+\frac{1}{24})\)
\(=\frac{1}{15}+\frac{11}{120}\)
\(=-\frac{1}{40}\)
Note: negative sign means emptying
Then volume of \(\frac{1}{40}\) part = 3 gallons
Volume of whole = 3 * 40 = 120 gallons
Correct option: C

“Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank in gallons is”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. 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.

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