Multiple choice

The ratio of milk and water in a mixture is 3 : 2. If 10 litres of water is added to it, the ratio gets reversed. What is the amount of the total mixture now?

  1. 10 litres

  2. 20 litres

  3. 24 litres

  4. 30 litres

  5. 32 litres
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D Correct answer
Explanation

Let the initial amounts be 3x and 2x. Adding 10 litres of water changes the ratio to 3x : (2x + 10), which equals 2 : 3. Solving 9x = 4x + 20 gives 5x = 20, so x = 4. The initial total was 5x = 20 litres, and adding 10 litres makes the new total 30 litres.

AI explanation

Let the initial quantities of milk and water be 3x and 2x respectively. Adding 10 litres of water makes the new ratio 2:3, giving the equation 3x divided by (2x plus 10) equals 2 divided by 3; solving this gives 9x equals 4x plus 20, so x is 4. The new total mixture is 3x plus 2x plus 10, which equals 12 plus 8 plus 10, resulting in 30 litres. The result is 30 litres.

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