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06 Jul 2020, 04:48
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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:
75%
(hard)
Question Stats:
62% (02:44) correct
38%
(02:50)
wrong
based on 452
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If 5 liters of water are added to a barrel when it is half full of water, the amount of water in the barrel will increase by \(\frac{2}{3}\). If x liters of water are then removed from the barrel, the amount of water in the barrel will decrease to \(\frac{2}{5}\) of the capacity of the barrel. What is the value of X?
A. 4
B. 4.5
C. 5
D. 6
E. 6.5
A. 4
B. 4.5
C. 5
D. 6
E. 6.5
06 Jul 2020, 04:56
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Bunuel
ANswer: Option E
Please check the image and Video solution for detail
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Screenshot 2020-07-06 at 5.25.38 PM.png [ 626.75 KiB | Viewed 8517 times ]
19 Sep 2020, 08:54
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Bunuel
Let v = the ORIGINAL volume of water in the tank (i.e., when the tank was HALF full)
If 5 liters of water are added to a barrel when it is half full of water, the amount of water in the barrel will increase by \(\frac{2}{3}\)
We can write: v + 5 = v + (2/3 of v)
In other words: v + 5 = v + 2v/3
Subtract v from both sides of the equation: 5 = 2v/3
Multiply both sides by 3 to get: 15 = 2v
Solve: v = 15/2 = 7.5
Important: Since v = the volume of water when the tank was HALF full, we can conclude that of the total CAPACITY of the barrel = 15 liters
Also important: Since we added 5 liters of water to the tank, the tank NOW contains 12.5 liters of water
If x liters of water are then removed from the barrel, the amount of water in the barrel will decrease to \(\frac{2}{5}\) of the capacity of the barrel.
We can write: 12.5 - x = 2/5 of 15
In other words: 12.5 - x = 6
Solve: x = 6.5
Answer: E
Cheers,
Brent
