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25 Apr 2023, 04:24
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
69% (02:38) correct
31%
(02:24)
wrong
based on 269
sessions
History
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A water tank has an inlet pipe which can fill the tank in 6 hours. One day the inlet pipe was opened and while closing the same after 6 hours it was found that a leakage has developed in the tank and tank was not filled to the capacity. The leakage was repaired immediately and the inlet pipe took 40 more minutes to fill the tank. How much time would the leakage take to empty the full tank when inlet pipe is not working.
A) 15 hours
B) 24 hours
C) 36 hours
D) 45 hours
E) 54 hours
A) 15 hours
B) 24 hours
C) 36 hours
D) 45 hours
E) 54 hours
25 Apr 2023, 05:02
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carcass
Let's assume that the volume of the tank is 6 gallons. Therefore, the rate at which the inlet pipe fills the tank is 1 gallon/hr.
6 hours after the inlet pipe was opened, the volume of water that was 'expected' to be filled in was 6 gallons. However, because of the leakage, some water was lost and the inlet pipe took \(\frac{40}{60}\) hours to fill the water that was lost because of the leakage.
In the \(\frac{2}{3}\) hour that the inlet pipe worked extra, \(\frac{2}{3}\) gallon of water was filled in. So we can infer that the leakage drained \(\frac{2}{3}\) gallon of water in 6 hours.
To drain 1 gallon of water the leakage would have taken \(\frac{3}{2} * 6 \) hours.
To drain out 6 gallons of water, the time that the leakage would have taken = \(\frac{3}{2} * 6 * 6 = 54 \) hours
Option E
25 Apr 2023, 09:44
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carcass
My instinct is to figure out how to set up an algebraic equation or two AND the answer choices are just numbers. When both of those things are true, Plugging In The Answers (PITA) is often at least as fast and much less mentally taxing. I generally like trying B and D, but I can see that things will be easier if I try answer choices that are multiples of 6, so I'll start with C and then do either B or E if C doesn't work.
C: Wouldn't it be nice to know how many gallons the tank is so we don't have to work with fractions of a tank? Okay, then let's just make something up (rather than working with partial jobs, treat a question like this as a Hidden Plug In...see my other posts tagged with that term)! Let's say the tank is 36 gallons. The leak loses 1 gallon per hour and the inlet pipe fills at 6 gallons per hour. In 6 hours, the inlet pipe fills 36 gallons and the leak loses 6 gallons, so we still need to fill 6 gallons. That will take 60 minutes. But we want it to take 40 minutes. We need a leak that let's out less water.
Between D and E, E looks easier to work with since it is a multiple of 6.
E: Let's say the tank is 54 gallons. The leak loses 1 gallon per hour and the inlet pipe fills at 9 gallons per hour. In 6 hours, the inlet pipe fills 54 gallons and the leak loses 6 gallons, so we still need to fill 6 gallons. That will take 6/9 hours, which is 40 minutes. That's what we wanted. Yay!
Answer choice E.
ThatDudeKnowsPITA
ThatDudeKnowsHiddenPlugIn
ThatDudeKnowsPlugginInTheAnswers
