Multiple choice

A solution contains some alcohol and some water in ratio 3 : 2. If another 200 ml of solution with equal proportion of alcohol and water is added to the given solution, ratio of alcohol to water becomes 4 : 3. What was the amount of water in initially given solution?

  1. 100 ml

  2. 150 ml

  3. 200 ml

  4. 300 ml

  5. 500 ml
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let initial alcohol be 3x and water be 2x. Total = 5x. Adding 200 ml of 1:1 solution means adding 100 ml alcohol and 100 ml water. New ratio: (3x + 100) / (2x + 100) = 4/3. 9x + 300 = 8x + 400 => x = 100. Initial water = 2x = 200 ml.

AI explanation

Let the initial volume of the solution be 5x, meaning it contains 3x of alcohol and 2x of water. Adding 200 ml of the second solution contributes 100 ml of alcohol and 100 ml of water, so the new total alcohol is 3x + 100 and the new total water is 2x + 100. The new ratio of alcohol to water is given as 4 to 3, so we solve the equation (3x + 100) divided by (2x + 100) equals 4 divided by 3, which gives 9x + 300 equals 8x + 400, meaning x equals 100. The initial amount of water was 2x, which equals 200 ml.

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