The ratio of milk to water in a 49-litre mixture is 4:3. Find the quantity (in…

Concept

When only one component is added to a two-component mixture, the quantity of the other, untouched component stays fixed. So to reach a target ratio, first find both components' quantities from the original ratio and total, then use the fixed component to solve for the added quantity.

Step-by-step solution

1. The mixture is 49 litres in the ratio milk : water = 4 : 3, so the total number of parts is 4 + 3 = 7.

2. Size of one part = 49 / 7 = 7 litres.

3. Milk quantity = 4 parts x 7 litres = 28 litres. Water quantity = 3 parts x 7 litres = 21 litres.

4. Let w litres of water be added. Only water is added, so the milk quantity stays at 28 litres while the water quantity becomes (21 + w) litres.

5. For the new ratio milk : water = 1 : 1, the two quantities must be equal: 28 = 21 + w.

6. Solving, w = 28 - 21 = 7 litres.

Cross-check

Adding 7 litres makes the water quantity 21 + 7 = 28 litres, equal to the unchanged milk quantity of 28 litres, so milk : water = 28 : 28 = 1 : 1, which matches the required ratio.