Multiple choice

A beaker contains acid and water in the ratio 1 : x, respectively. When 300 ml of the mixture and 50 ml of water are mixed, the ratio of acid to water becomes 2 : 5. What is the value of x?

  1. 2

  2. 1

  3. 3

  4. 4
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A Correct answer
Explanation

In 300 ml of mixture, the acid-to-water ratio is 1:x. After adding 50 ml water, setting the new ratio to 2:5 gives x = 2.

AI explanation

From the 300 ml of mixture taken, the amount of acid is 300 / (1 + x) and the amount of water is 300x / (1 + x). Adding 50 ml of water makes the new water volume (300x / (1 + x)) + 50. Setting the new ratio of acid to water gives the equation (300 / (1 + x)) / ((300x / (1 + x)) + 50) = 2 / 5. Cross multiplying and simplifying results in 1500 = 700x + 100, which solves to x = 2.

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