Ratio and Proportion: A Flask contains a mixture of 98 litres of alcohol and water in the proportion 5:2. How much water (in liters) must be added to it so that the ratio of alcohol to water may be 7:5?

Step 1: Break down the initial mixture

Total = 98 litres Ratio of alcohol to water = 5:2 Total parts = 5 + 2 = 7 Each part = 98 ÷ 7 = 14 litres

So:

Alcohol = 5 × 14 = 70 litres

Water = 2 × 14 = 28 litres

Step 2: Add x litres of water

New water amount = 28 + x Alcohol remains = 70 litres

We want the new ratio to be 7:5: → 70 / (28 + x) = 7 / 5

Cross-multiply: 5 × 70 = 7 × (28 + x) → 350 = 196 + 7x → 7x = 154 → x = 22 litres