A mixture contains alcohol and water in the ratio 4 : 3. If 5 litres of water is added, the ratio becomes 4 : 5. Find the quantity of alcohol in the original mixture.

Introduction / Context:
This is a classic mixture and ratio problem involving two components, alcohol and water. The initial ratio of quantities is given, then some additional water is added and the ratio changes. From the change in ratio, we must find the absolute quantity of alcohol that was present in the mixture before adding the water.

Given Data / Assumptions:
- Initially, the ratio of alcohol to water is 4 : 3. - After adding 5 litres of water, the ratio becomes 4 : 5. - Volumes are additive, and there is no loss or evaporation. - We must find the quantity of alcohol in litres in the original mixture.

Concept / Approach:
Let alcohol and water initially be 4x and 3x litres. Adding 5 litres of water changes only the water term. The new ratio condition gives an equation involving x. Solving that equation yields the volumes of both components. This is a standard approach in ratio problems: use a common multiplier to represent the actual quantities.

Step-by-Step Solution:
Step 1: Let initial quantity of alcohol = 4x litres and initial quantity of water = 3x litres. Step 2: After adding 5 litres of water, alcohol remains 4x litres, water becomes 3x + 5 litres. Step 3: New ratio of alcohol to water is 4 : 5, so 4x : (3x + 5) = 4 : 5. Step 4: Convert ratio to an equation: 4x / (3x + 5) = 4 / 5. Step 5: Cross multiply: 4x * 5 = 4 * (3x + 5). Step 6: This gives 20x = 12x + 20. Step 7: Subtract 12x from both sides: 8x = 20. Step 8: So x = 20 / 8 = 2.5. Step 9: Quantity of alcohol = 4x = 4 * 2.5 = 10 litres.

Verification / Alternative check:
Using x = 2.5, initial water is 3x = 7.5 litres. After adding 5 litres, water becomes 7.5 + 5 = 12.5 litres. The new ratio alcohol : water is 10 : 12.5. Both numbers divide by 2.5 to give 4 : 5, matching the ratio given in the problem. This confirms that the calculated quantity of alcohol, 10 litres, is correct.

Why Other Options Are Wrong:
- 12, 15 and 18 litres: Each of these would lead to different ratios after adding 5 litres of water, and none of those ratios would simplify exactly to 4 : 5.

Common Pitfalls:
Some students incorrectly add 5 litres to both components or assume that the total volume is unchanged, which is not true when more liquid is added. Others set up the ratio with denominators reversed. The safe method is always to use variables for the components, adjust only the relevant component when something is added or removed, then translate the new ratio into an equation and solve carefully.

Final Answer:
The original mixture contains 10 litres of alcohol.