Mixture Problem

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

Guess the soultion above is the simplest but here my way to it

Let X be the total quantity
Let Y be the replaced quantity

Fraction n = Y/X . Hence the Y = nX

The problem translates to this equation

0.4X- n(0.4X) + 0.25nX = 0.35X

If you solve this equation n = 1/3.

Hope this helps.

Alternative explanation and approach for the same.

No. of liters of original solution = x
No. of liters replaced = y

*** NOTE that the solution is REPLACED, which means that the quantity of the resulting mixture is still same as the original solution. In this case, the quantity of resulting mixture will still be x ****

put in the equation

40% of (x - y) + 25 % y = 35 % of x

2/5 * (x - y) + y/4 = 7x/20

solving, you will get y/x = 1/3

40%.....35%.......25 %

40-35=5
35-25=10

replacement : 5/15