1. **State the problem:** We have 1 litre of fruit drink made by mixing cordial and water in the ratio 1:7. 2. **Initial quantities:** Since the total is 1 litre and the ratio is 1:7, the cordial amount is $ \frac{1}{1+7} = \frac{1}{8} $ litres and water amount is $ \frac{7}{8} $ litres. 3. **Goal:** Add some water $ x $ litres to make the new ratio of cordial to water 3:25. 4. **Set up the equation:** After adding water, cordial remains $ \frac{1}{8} $ litres, water becomes $ \frac{7}{8} + x $. The ratio is $ \frac{\text{cordial}}{\text{water}} = \frac{3}{25} $, so: $$ \frac{\frac{1}{8}}{\frac{7}{8} + x} = \frac{3}{25} $$ 5. **Solve for $ x $:** Multiply both sides by $ \frac{7}{8} + x $: $$ \frac{1}{8} = \frac{3}{25} \left( \frac{7}{8} + x \right) $$ Multiply both sides by 25: $$ 25 \times \frac{1}{8} = 3 \left( \frac{7}{8} + x \right) $$ Simplify left side: $$ \frac{25}{8} = 3 \left( \frac{7}{8} + x \right) $$ Divide both sides by 3: $$ \frac{25}{8} \times \frac{1}{3} = \frac{7}{8} + x $$ $$ \frac{25}{24} = \frac{7}{8} + x $$ Subtract $ \frac{7}{8} $ from both sides: $$ x = \frac{25}{24} - \frac{7}{8} $$ Find common denominator 24: $$ x = \frac{25}{24} - \frac{21}{24} = \frac{4}{24} = \frac{1}{6} $$ 6. **Answer:** The amount of water to add is $ \frac{1}{6} $ litres. **Final answer:** $ \boxed{\frac{1}{6} \text{ litres}} $