A certain tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride.

BTGmoderatorDC wrote: ↑

Sat May 23, 2020 9:24 pm

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 Prep

Given that the tank is filled to one-quarter of its capacity with the mixture consisting of water and sodium chloride, the amount of the mixture = 1/4 of 24 = 6 gallons

Amount of sodium = 40 % of 6 gallons = 2.4 gallons

=> Amount of water = 6 – 2.4 = 3.6 gallons

Given that the water evaporates from the tank at the rate of 0.5 gallons per hour, in 2 hours, 0.5*2 = 1 gallon water would be evaporated.

Thus, water left now = 3.6 – 1 = 2.6 gallons

Amount of mixture = 6 – 1 = 5 gallons

The concentration of water in the mixture in 2 hours = (2.6/5)*100% = 52%

The correct answer: C

Hope this helps!

-Jay
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BTGmoderatorDC wrote: ↑

Sat May 23, 2020 9:24 pm

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

Solution:

Since the capacity of the tank is 24 gallons, one quarter of its capacity is 6 gallons and 0.4 x 6 = 2.4 gallons is sodium chloride and 6 - 2.4 = 3.6 gallons is water. Since water evaporates at a rate of 0.5 gallons per hour, 1 gallon of water will evaporate in 2 hours. Therefore, we are left with 2.6 gallons of water and 6 - 1 = 5 gallons of mixture in the tank. Therefore, the concentration of water in the mixture after 2 hours is 2.6/5 = 26/50 = 52/100 = 52%.

Answer: C