In a pot there is a mixture of milk and water in the ratio 4 : 5. If an additional 8 litres of pure milk is poured into the pot, the pot becomes completely full and the ratio of milk to water changes to 6 : 5. What is the total capacity of the pot in litres?

Introduction:
This mixture question deals with changing the ratio of milk to water in a container when extra milk is added. It uses the concept of ratios and basic algebra to relate the initial and final quantities and to determine the total capacity of the pot.

Given Data / Assumptions:

• Initially the pot contains a mixture of milk and water in the ratio 4 : 5.
• Only milk and water are present in the mixture.
• 8 litres of pure milk are added to the pot.
• After adding the milk, the pot becomes full.
• The new ratio of milk to water becomes 6 : 5.
• We are asked to find the total capacity of the pot in litres.

Concept / Approach:
We use the idea of ratio representation. If a mixture has milk and water in the ratio 4 : 5, we can represent milk as 4k litres and water as 5k litres. When 8 litres of pure milk are added, only the milk quantity changes, while the amount of water remains the same. The final ratio becomes 6k1 : 5k1, but here we can directly set up an equation using the new ratio 6 : 5 and solve for k and for the pot capacity.

Step-by-Step Solution:
Step 1: Let the initial quantities be milk = 4k litres and water = 5k litres. Step 2: The initial total mixture is 4k + 5k = 9k litres. Step 3: 8 litres of pure milk are added, so the new milk quantity is 4k + 8 litres, water remains 5k litres. Step 4: The new ratio of milk to water is given as 6 : 5. Step 5: Set up the equation (4k + 8) / 5k = 6 / 5. Step 6: Cross multiply: 5 * (4k + 8) = 6 * 5k. Step 7: This gives 20k + 40 = 30k. Step 8: Rearrange: 30k - 20k = 40, so 10k = 40, hence k = 4. Step 9: Initial volume = 9k = 9 * 4 = 36 litres. Step 10: After addition, total capacity = 36 + 8 = 44 litres.

Verification / Alternative check:
With k = 4, initial milk = 16 litres, water = 20 litres. After adding 8 litres of milk, milk becomes 24 litres, water remains 20 litres. The ratio 24 : 20 simplifies to 6 : 5, confirming that the algebra is correct and that the total capacity of the pot is 44 litres.

Why Other Options Are Wrong:
11 litres and 22 litres: These values are far less than the volume already present after adding 8 litres of milk, and they do not satisfy the ratio conditions.
33 litres: This would imply an initial volume too small to maintain the given ratios after adding 8 litres of milk.
36 litres: This is the initial volume before adding 8 litres, not the full pot capacity. The question specifically asks for the capacity when full, which is 36 + 8 = 44 litres.

Common Pitfalls:
A frequent error is to forget that only milk is added, so the water quantity remains unchanged. Another mistake is treating 8 litres as part of the ratio units directly, instead of using a variable k. Some learners also misinterpret the phrase that the pot becomes full and think they must change the total and the ratio in arbitrary ways rather than using a clear algebraic setup.

Final Answer:
The total capacity of the pot is 44 litres.