A certain tank is filled to one quarter of its capacity with a mixture

Question

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%

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

PareshGmat · Accepted Answer

Answer = C = 52%

NaCl................... Water ................. Total

2.4 ......................... 3.6 ....................... 6

Post evaporation

2.4 ........................... 2.6 ......................... 5

Percentage  = \frac{2.6}{5} * 100 = 52%

KarishmaB · Answer

The tank of 24 gallons is filled to a quarter so it had 6 gallons of water with 40% sodium chloride. In 2 hrs, .5*2 = 1 gallon of pure water (0% sodium chloride) will evaporate. 
In essence, the initial mix of 6 gallons (40% sodium chloride) was a mix of 5 gallons of x% sodium chloride and 1 gallon of pure water.

Working with sodium chloride concentrations:
w1/w2 = (A2 - Aavg)/(Aavg - A1)
5/1 = (0 - 40)/(40 - x)
x = 48

So concentration of water is 100 - 48 = 52%

navaljoshi · Answer

c - initial 40% sodium = 2.4 & 60 % water = 3.6 after 2 hours- evaporating at the rate of .5/hr sodium -2.4 ,water -2.6 c- 52% Hope i deserve some kudos

DesiGmat · Answer

Tank is filled 1/4 of its capacity

Solution = 1/4 * 24 = 6

Sodium = 0.4 * 6 = 2.4
Water = 6-2.4 = 3.6

Evaporation Process

0 hour - 3.6
1 hour - 3.1
2 hour - 2.6

or you can simply subtract 1 from 3.6

quantity of new solution = sodium + water = 2.4 + 2.6 = 5

Concentration of water = (2.6/5) * 100 = 52%

lalania1 · Answer

Here is how I did it. My mistake when i first tried it was forgetting that the tank is 1/4 full and that i needed to divide 24/4 in order to get the correct solution.

step1) (1/4) 24 = 6
step2) 6*(.40) =SC = 2.4 and 6*(.6) = W = 3.6 = total = 6
step3) 0.5*2 = 1 => 6-1 = 5 new total => 3.6 -1 = 2.6 new water
step4) 2.6/5 => (2.6*2)/(5*2) = 5.2/10 = 0.52.

yezz · Answer

SINCE THE amount of SC didn't change we can use the formula (C final = C initial * V initial/V final)

Cf = 0.4* (6/5.5)*(5.5/5) = 48% and thus water concentration in final mix is 100%-48% 52%

ScottTargetTestPrep · Answer

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

Basshead · Answer

The capacity of the tank is 24 gallons. We are told the tank is only filled to one quarter of its capacity, meaning its filled to 6 gallons.

The proportion of sodium chloride is 40% by volume; thus, out of the 6 gallons, 2.4 gallons is sodium chloride.

We're then told water evaporates from the tank at the rate of 0.5 gallons per hour. In two hours, one gallon will have evaporated.

We're left with 5 gallons, of which 2.4 gallons is sodium chloride.

5 * 2 = 10
2.4 * 2 = 4.8
10 - 4.8 = 5.2
5.2 = 52%

Answer is C.

bumpbot · Answer

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A certain tank is filled to one quarter of its capacity with a mixture

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A certain tank is filled to one quarter of its capacity with a mixture

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