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Apr 2808:00 AM PDT
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27 Apr 2020, 09:59
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C
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Difficulty:
95%
(hard)
Question Stats:
47% (02:11) correct
53%
(02:21)
wrong
based on 242
sessions
History
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A pump takes 4 hours to fill an empty pool. If the pump increased the water level of the pool to 80 percent of its total capacity after pumping water for 1 hour and 30 minutes, what percent of the pool was empty before the pump started working?
A: 37.5%
B: 42.5%
C: 57.5%
D: 62.5%
E: 70.0%
A: 37.5%
B: 42.5%
C: 57.5%
D: 62.5%
E: 70.0%
27 Apr 2020, 11:03
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Approach
Assume total capacity of Pool = 100 L
Pump's capacity to fill pool in 1 hr : 25L or 25% of pool
..................................... in 1.5 hr : 37.5L or 37.5% of pool.
Given is after 1.5 hrs of pump start, Pool is filled to 80% of capacity i.e. 80L.
So, percent of the pool was empty before the pump started working: 100 - (80-37.5) = 57.5%
Option C
Assume total capacity of Pool = 100 L
Pump's capacity to fill pool in 1 hr : 25L or 25% of pool
..................................... in 1.5 hr : 37.5L or 37.5% of pool.
Given is after 1.5 hrs of pump start, Pool is filled to 80% of capacity i.e. 80L.
So, percent of the pool was empty before the pump started working: 100 - (80-37.5) = 57.5%
Option C
28 Apr 2020, 06:12
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Let the capacity of the pool be 1 litre. It takes 4 hours to fill 1 litre.
Therefore, rate of filling is \(\frac{1}{4}\) litres per hour. At this rate, if it works for 1 hour 30 minutes i.e. \(\frac{3}{2}\) hours,
Quantity of water filled = \(\frac{1}{4}\) * \(\frac{3}{2}\) = \(\frac{3 }{ 8}\) litres
When the above quantity was filled, the tank is 80% full i.e. it has \(\frac{4}{5}\) litres. Therefore, the difference between the two will tell us how much water was already there in the pool.
Difference = \(\frac{4}{5}\) – \(\frac{3}{8}\) = \(\frac{32 – 15 }{ 40}\) = \(\frac{17 }{ 40}\) * 100 = 42.5%. Because there was 42.5% in the pool already, we can say that the pool was 57.5% empty when the pump started working.
The correct answer option is C.
Hope that helps!
Therefore, rate of filling is \(\frac{1}{4}\) litres per hour. At this rate, if it works for 1 hour 30 minutes i.e. \(\frac{3}{2}\) hours,
Quantity of water filled = \(\frac{1}{4}\) * \(\frac{3}{2}\) = \(\frac{3 }{ 8}\) litres
When the above quantity was filled, the tank is 80% full i.e. it has \(\frac{4}{5}\) litres. Therefore, the difference between the two will tell us how much water was already there in the pool.
Difference = \(\frac{4}{5}\) – \(\frac{3}{8}\) = \(\frac{32 – 15 }{ 40}\) = \(\frac{17 }{ 40}\) * 100 = 42.5%. Because there was 42.5% in the pool already, we can say that the pool was 57.5% empty when the pump started working.
The correct answer option is C.
Hope that helps!
