Question: A pool can be filled in 4 hours and drained in 5 hours. The valve that fills the pool was opened at 1:00 PM and sometime late the drain that empties the pool was also opened. If the pool was filled by 11:00 PM and not earlier, when was the drain opened?

1. At 2:00 PM
2. At 2:30 PM
3. At 3:00 PM
4. At 3:30 pm
5. At 4:00 PM

Correct Answer: (D)

Solutions and Explanation

Approach Solution (1):

When only the valve is open, the pool is filling at a rate of \(\frac{1}{4}\) an hour. When both the valve and the drain is open, the pool is filling at a rate of \(\frac{1}{4}-\frac{1}{5}=\frac{1}{20}\) an hour. Let x denote the time when only the valve was open. Then both the valve and the drain were open for 11 – 1 – x = 10 – x hours.

Now we can compose the equation: \(\frac{1}{4}x+\frac{1}{20}(10-x)=1\) which reduces to \(\frac{x}{5}=0.5\) from where x = 2.5.

Thus, the drain was opened at 1:00 + 2:30 = 3:30 PM

Approach Solution (2):

The valve that fills is working at a e=rate of ¼ per hour

The drain is working at a rate of 1/5 per hour

Not the valve is open for 10 hours (between 1 PM to 11 PM)

Let the drain be open for x hours

So work done is 10/4 (valve’s work)

Drain work is x/5

10/4 – x/5 = 1 (assuming work is 1)

Gives us x = 7.5 hours

Drain was open for 7.5 hours which is 2.5 hours from 1 PM = 3:30 PM

Approach Solution (3) :

Consider the overall work = 100%.

Each hour's output for filling A is 25% (Work completed in 1 hour is 25% of the total 4 hours of work.)

Work by Drain (B) = –20% (negative because it goes against the flow of the tank filling naturally; 20% is found as before).

Consider the filling time as x, then the combined time of A and B is, 10 - x

Work is now evaluated as time multiplied by a rate.

Which implies, 100% = 25*x + (25-20=5) *(10-x) (10-x)

x=2.5 hours after solving

As a result, the drain was opened 2.5 hours after A. As a result, the drain was opened at 1:30 +2.5 hrs =3:30 p.m.

“A pool can be filled in 4 hours and drained in 5 hours. The valve that fills the pool was opened at 1:00 PM and sometime late the drain that empties the pool was also opened. If the pool was filled by 11:00 PM and not earlier, when was the drain opened?”- 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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