In a 48 litre mixture, the ratio of milk to water is 5 : 3. How many litres of water must be added to this mixture so that the ratio of milk to water becomes 3 : 5 in the final mixture?

Introduction:
This question involves changing the ratio of milk to water in a mixture by adding water only. Initially, milk is in higher proportion, and we want water to become dominant, so more water must be added. The problem tests skills in ratio handling and algebraic manipulation in mixture situations.

Given Data / Assumptions:

• Total initial mixture volume = 48 litres.
• Initial ratio of milk to water = 5 : 3.
• Only water is added, milk quantity remains unchanged.
• After adding water, the ratio of milk to water becomes 3 : 5.
• We must find how many litres of water are added.

Concept / Approach:
We first determine the initial volumes of milk and water from the given ratio. Then we let x be the amount of water added. Milk remains constant, while water increases by x. Using the final ratio, we create an equation and solve for x. This is a standard application of ratio algebra in mixtures.

Step-by-Step Solution:
Step 1: Initial total mixture = 48 litres with milk : water = 5 : 3. Step 2: Total parts = 5 + 3 = 8 parts. Step 3: Milk initially = 48 * 5 / 8 = 30 litres. Step 4: Water initially = 48 * 3 / 8 = 18 litres. Step 5: Let x litres of water be added to the mixture. Step 6: Milk after addition = 30 litres (unchanged). Step 7: Water after addition = 18 + x litres. Step 8: The final ratio of milk to water is 3 : 5, so: 30 / (18 + x) = 3 / 5. Step 9: Cross multiply: 30 * 5 = 3 * (18 + x). Step 10: This gives 150 = 54 + 3x. Step 11: Subtract 54 from both sides: 96 = 3x. Step 12: So x = 96 / 3 = 32 litres.

Verification / Alternative check:
After adding 32 litres of water, water amount becomes 18 + 32 = 50 litres. New total volume = 30 litres milk + 50 litres water = 80 litres. New ratio of milk to water = 30 : 50, which simplifies to 3 : 5 as required. Thus the calculation is consistent and correct.

Why Other Options Are Wrong:
24 litres or 16 litres: These give water amounts of 42 litres or 34 litres respectively, leading to ratios that are not equal to 3 : 5.
8 litres and 20 litres also produce final ratios that do not simplify to 3 : 5 when combined with the unchanged 30 litres of milk.

Common Pitfalls:
Common errors include changing the milk quantity along with water when only water is added, or attempting to scale the ratio directly without accounting for the absolute volumes. Another mistake is cross multiplying incorrectly when setting up the ratio equation, which can lead to incorrect values of x.

Final Answer:
The amount of water that must be added is 32 litres.