Jar A contains 36 litres of a milk-water mixture in the ratio 5:4 (milk:water). Jar B contains 20 litres of a milk-water mixture (composition unknown). Jar B is completely emptied into Jar A. After mixing, the ratio of milk to water in Jar A becomes 5:3. What was the quantity of water (in litres) present in Jar B before pouring it into Jar A?

Introduction / Context:
This is a mixture combination problem where one mixture is known and the other mixture is unknown. The key strategy is to convert Jar A ratio into exact litres of milk and water, then represent Jar B milk and water as variables that sum to 20 litres. After combining, the final ratio is given (5:3), which creates an equation relating total milk and total water. Solving that equation gives the water in Jar B.

Given Data / Assumptions:

• Jar A volume = 36 litres, milk:water = 5:4
• Jar B volume = 20 litres, composition unknown
• Jar B is fully poured into Jar A
• Final milk:water ratio = 5:3
• Let water in Jar B = w and milk in Jar B = m
• m + w = 20

Concept / Approach:
Compute milk and water in Jar A from ratio 5:4. Then write total milk and total water after mixing as (milkA + m) and (waterA + w). Use the final ratio equation (total milk)/(total water) = 5/3. Substitute m = 20 - w and solve for w.

Step-by-Step Solution:
Jar A total parts = 5 + 4 = 9 Milk in A = (5/9) * 36 = 20 litres Water in A = (4/9) * 36 = 16 litres After adding Jar B: total milk = 20 + m, total water = 16 + w Final ratio 5:3 => (20 + m)/(16 + w) = 5/3 m + w = 20 => m = 20 - w (20 + 20 - w)/(16 + w) = 5/3 (40 - w)/(16 + w) = 5/3 3*(40 - w) = 5*(16 + w) 120 - 3w = 80 + 5w 40 = 8w w = 5 litres

Verification / Alternative check:
If w=5, then m=15. Totals become milk=20+15=35 and water=16+5=21. Ratio 35:21 simplifies to 5:3, matching the final condition exactly.

Why Other Options Are Wrong:
2 or 3 litres makes Jar B too milk-heavy, increasing the final ratio above 5:3. 7 or 8 litres adds too much water, reducing the final ratio below 5:3.

Common Pitfalls:
Mixing up milk and water quantities from 5:4, forgetting that Jar B is completely poured, or applying the final ratio to Jar B only instead of to the combined totals.

Final Answer:
Jar B initially contained 5 litres of water.