If 5 liters of water are added to a barrel when it is half full of wat

Question

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

GMATinsight · Answer

ANswer: Option E

Please check the image and Video solution for detail

https://www.youtube.com/watch?v=vRGF35YSGtc

BrentGMATPrepNow · Answer

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

Kinshook · Answer

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

What is the value of X?

Let the capacity of the barrel be 30L liters

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} . 
5 litres of water are added to a barrel when it is 15L litres of water, the amount of water in the barrel will increase by 2/3*15L = 10L
10L = 5
L = .5 liters

The capacity of the barrel = 15 liters

Water available in the barrel = 7.5 + 5 = 12.5 liters

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. 
2/5 of the capacity of the barrel = 2/5*15 = 6 liters

Water removed form the barrel = x = 12.5 - 6 = 6.5 liters

IMO E

bumpbot · Answer

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If 5 liters of water are added to a barrel when it is half full of wat

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