Question: An inlet pipe can fill in an empty cistern in 30 minutes whereas a leak in the bottom of the cistern can empty a filled tank in 40 minutes. Find the time taken to fill the cistern when both the inlet pipe and the leak are on.
- 120 minutes
- 125 minutes
- 130 minutes
- 135 minutes
- 140 minutes
“An inlet pipe can fill in an empty cistern in 30 minutes”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT 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.
Approach Solution 1:
Considering the given case scenario in the question, it can be seen that an inlet pipe is able to fill in an empty cistern in 30 minutes. On the other hand, with the presence of a leak on the bottom of the cistern, the time taken to fill the empty tank takes 40 minutes. With both the inlet pipe and the leak being present to be filled the tank, the case is to find the time taken to fill the tank.
Accordingly, the time taken by the inlet pipe to fill the empty cistern is 30 minutes. This implies the time taken by the inlet pipe to fill the cistern in 1 minutes is equal to 1/30.
Similarly, with the presence of a leak in the bottom of the cistern, the time taken to fill the tank is 40 minutes. This means that the time taken by the cistern with a leakage to fill the tank each minute is equal to 1/40.
To find the time taken by both the inlet pipe and the leakage in the cistern together to fill the tank, it is necessary to assume that the time is x. To find the time , the following problem needs to be solved. This is by subtracting each minute by the total number of minutes in combination of both inlet pipe and leakage cistern.
Let the time be x. So the time taken by both inlet pipe and leakage in the cistern to fill the tank for each minute would be 1/x. Accordingly, the following equation would help in finding the time as follows:
\(\Rightarrow \frac{1}{x} = \frac{1}{30}-\frac{1}{40}\)
\(\Rightarrow\frac{1}{x}=\frac{4-3}{120}\)
\(\Rightarrow \frac{1}{x}= \frac{1}{120}\)
\(\Rightarrow x= 120\)
Thus, from the resolving of the above equation, x has been formulated as 120. This implies that with both the inlet pipe and the leakage in the cistern being on, it takes 120 minutes for the tank to be filled completely.
Correct Answer: A
Approach Solution 2:
Considering the given case scenario in the question, it can be seen that an inlet pipe is able to fill in an empty cistern in 30 minutes. On the other hand, with the presence of a leak on the bottom of the cistern, the time taken to fill the empty tank takes 40 minutes. Accordingly, combining both the times it is possible to evaluate both the aspects.
This can be done as follows:
\(\frac{1}{30}-\frac{1}{40}=\frac{1}{120}\)
Hence, the correct answer is 120 minutes.
Correct Answer: A
Approach Solution 3:
It is clear from the example study provided in the question that an inlet line may fill an empty cistern in 30 minutes. The time it takes to fill the empty tank, on the other hand, is increased by 40 minutes due to a leak in the cistern's bottom. In light of this, it is feasible to evaluate both features by combining the two times.
Here's how to go about it:
\(\frac{1}{30}-\frac{1}{40}=\frac{1}{120}\)
Therefore, 120 minutes is the right answer.
Correct Answer: A
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