Question

Brine is a solution of salt and water. If a tub contains 50 gallons of a 5% solution of brine, how much water must evaporate to change it to an 8% solution?

A.81.25 gallons

B.62.50 gallons

C.18.75 gallons

Answer 1

The answer would be C, 18.75 gallons.

Answer 2

C. 18.75 gallons

Explanation:

Given,

Total solution = 50 gallons,

The quantity of brine in the solution = 5 % of 50 = 2.5 gallons,

And, the original quantity of water in the solution = Total solution - Brine

= 50 - 2.5 = 47.5 gallon,

Let x be the quantity of water that must evaporate to change it to an 8% solution,

Also, the ratio of the brine and water in the resultant solution = 8 : 92

So, we can write,

`(2.5)/(47.5-x)=(8)/(92)`

`230=380-8x` ( By cross multiplication )

`8x = 380 - 230 = 150`

`\implies x = (150)/(8)=18.75`

Hence, 18.75 gallons of water must evaporate to change the percentage of brine from 5 % an 8 %.

Option C is correct.