Multiple choice

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?

  1. 1/4

  2. 1/3

  3. 1/2

  4. 2/3

  5. 3/4
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let x be the fraction replaced. New concentration = (1-x)*0.40 + x*0.25 = 0.35. 0.40 - 0.15x = 0.35. 0.05 = 0.15x. x = 0.05 / 0.15 = 1/3.

AI explanation

Using the method of alligation, we can find the ratio of the remaining original solution to the added solution. Place the initial concentration of 40% and the replacement concentration of 25% on the left, with the target mixture concentration of 35% in the middle. The ratio is calculated as (35 minus 25) to (40 minus 35), which equals 10 to 5, or 2 to 1. This means the final mixture consists of 2 parts of the original solution and 1 part of the new solution, making the total 3 parts. Since the added new solution is 1 part out of the 3 total parts, the fraction of the solution that was replaced is 1/3.

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