Problem Solving

7. A certain quantity of 40% solution is replaced with 25% solution such that the new concentration is 35%. What is the fraction of the solution that was replaced?
(A) 1/4
(B) 1/3
(C) 1/2
(D) 2/3
(E) ¾

please help me with a simple method!!

Is the answer B?

If it is correct, I have a very simple solution.

let x be the fraction replaced. if x is the fraction then the total is 1.

(1-x)*40 + x*25 = 35
40 - 40x + 25x = 35
5 = 15x
x = 1/3

You may use allegation to solve this quickly:

40% 25%

35%

(35-25) (40-35)

So the 2 solutions need to be mixed in a ratio of (35-25):(40-35) or 2:1 Bingo! U'r done!

So, 2/3 is 40% soln and 1/3 is 25% which implies, 1/3 of the soln needs to be replaced.

Plug in 100 (can be gallons, liters, anything) for total amount:

.25x+.40(100-x)=.35(100)
.25+40-.40x=35
-.15x=-5
x=33.3

This solution for x tells us that 33.3/100, or 1/3, of the solution is 25%, or the amount that was replaced. Answer: B

raunekk wrote:7. A certain quantity of 40% solution is replaced with 25% solution such that the new concentration is 35%. What is the fraction of the solution that was replaced?
(A) 1/4
(B) 1/3
(C) 1/2
(D) 2/3
(E) �

please help me with a simple method!!

As noted in a post above, alligation is a great way to solve mixture problems. According to alligation:

The proportion of each element in the mixture is equal to the distance between the percentage attributed to the other element in the mixture and the percentage attributed to the mixture.

Proportion of the 40% solution = |percentage in mixture - percentage in the other solution| = |35-25| = 10.
Proportion of the 25% solution = |percentage in the mixture - percentage in the other solution| = |35-40| = 5.
Ratio of 40% solution : 25% solution = 10:5 = 2:1.

Thus, for every 2 parts 40% solution, we need 1 part 25% solution.
Since 1 of every 3 parts must be the 25% solution, 1/3 of the solution must be replaced.

The correct answer is B.