In a mixture of 36 litres the ratio of milk and water is 5:1. If x litres of…

Concept: In a mixture problem, a ratio describes how a fixed total splits into named parts, so the actual quantity of each ingredient equals its ratio-share of the total. When one ingredient's quantity is held fixed and more of the other is mixed in, the new ratio is found by writing the fixed quantity over the changed ingredient's new quantity and equating that to the new ratio.

Application:

1. The 36-litre mixture has milk and water in the ratio 5:1, so total parts = 5 + 1 = 6, and each part = 36 ÷ 6 = 6 litres.

2. Milk = 5 × 6 = 30 litres, and water = 1 × 6 = 6 litres.

3. Only water is increased, by x litres; milk stays fixed at 30 litres, so the new water quantity is (6 + x) litres.

4. The resultant ratio of milk to water is given as 3:2, so 30 / (6 + x) = 3 / 2.

5. Cross-multiplying: 30 × 2 = 3 × (6 + x), which gives 60 = 18 + 3x.

6. So 3x = 60 − 18 = 42, and x = 42 ÷ 3 = 14.

Cross-check: With x = 14, the new water quantity is 6 + 14 = 20 litres, and milk : water = 30 : 20 = 3 : 2, which matches the ratio stated in the question.