Problem Solving

A certain tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride. The proportion of sodium chloride in the tank is 40% by volume and the capacity of the tank is 24 gallons. If the water evaporates from the tank at the rate of 0.5 gallons per hour, and the amount of sodium chloride stays the same, what will be the concentration of water in the mixture in 2 hours?

A.43%
B.50%
C.52%
D.54%
E.56%

OA C

Source:Manhattan GMAT

selango wrote:A certain tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride. The proportion of sodium chloride in the tank is 40% by volume and the capacity of the tank is 24 gallons. If the water evaporates from the tank at the rate of 0.5 gallons per hour, and the amount of sodium chloride stays the same, what will be the concentration of water in the mixture in 2 hours?

A.43%
B.50%
C.52%
D.54%
E.56%

OA C

Source:Manhattan GMAT

the capacity of the tank is 24
So 6 gallons is filled with the mixture.
40% of 6 gallaons is 2.4 gallons
after 2 hours 1 gallon of water will evaporate.
so remaining water is 6-2.4-1 = 2.6
so percentage = 2.6/3 * 100= 52%

pick C

Guys,
A small correction to the above post by Kvcpk.

the capacity of the tank is 24
So 6 gallons is filled with the mixture.
40% of 6 gallaons is 2.4 gallons
after 2 hours 1 gallon of water will evaporate.
so remaining water is 6-2.4-1 = 2.6

After 1 gallon water evaporation, the total gallons of mixture would be=6-1=5 gallons.
so percentage = 2.6/5 * 100= 52%

C

sanabk wrote:Guys,
A small correction to the above post by Kvcpk.

the capacity of the tank is 24
So 6 gallons is filled with the mixture.
40% of 6 gallaons is 2.4 gallons
after 2 hours 1 gallon of water will evaporate.
so remaining water is 6-2.4-1 = 2.6

After 1 gallon water evaporation, the total gallons of mixture would be=6-1=5 gallons.
so percentage = 2.6/5 * 100= 52%

C

why do we do this : 6-1-2.4?
why not just 6-1 and 2.4/5*100?
thanks!

raunakrajan wrote:
why do we do this : 6-1-2.4?
why not just 6-1 and 2.4/5*100?
thanks!

Hi, 2.4 is the amount of NACL and not water.

Question is asking for concentration of water.


@sanabk - Thanks for the correction--Thant was a typo

24 gallons
quantity filled in the tank is 1/4*24=6
sodium chloride is 40%=2.4
water=3.6

after 2 hours, water=2.6
5 gallons of liquid remains in tank after 2 hours

5 gallons - 100%
2.6 - ?
?=52%

1/4 of 24 gallons = 6

40% of 6 = 2.4 gallons sodium
60% of 6 = 3.6 gallons water

per hr .5 gallon of water evaporates
2 hrs = .5 * 2 = 1 gallon

so water = 3.6 - 1 = 2.6

and total gallons = 6 - 1 = 5

So % of water in 5 gallons = 52%