In a mixture, the ratio of juice to water is 4 : 3. After adding 6 litres of water, the ratio of juice to water becomes 8 : 7.\nWhat is the amount of juice (in litres) in the original mixture before adding the extra water?

Introduction:
This is a ratio-change problem where only water is added. When water is added, the juice quantity remains constant while water quantity increases. We represent original quantities using a common multiplier, apply the new ratio condition, and solve for the multiplier to find the original juice amount.

Given Data / Assumptions:

• Original juice : water = 4 : 3
• Water added = 6 litres
• New juice : water = 8 : 7
• Juice amount stays the same

Concept / Approach:
Let original juice = 4k and original water = 3k. After adding 6 litres water, water becomes 3k + 6. The ratio becomes:\n4k : (3k + 6) = 8 : 7.\nSolve for k, then compute juice = 4k.

Step-by-Step Solution:
Assume original juice = 4kAssume original water = 3kAfter adding water: new water = 3k + 6New ratio condition: 4k / (3k + 6) = 8/7Cross-multiply: 7 * 4k = 8 * (3k + 6)28k = 24k + 484k = 48k = 12Original juice = 4k = 4 * 12 = 48 litres

Verification / Alternative Check:
Original water = 3k = 36 litres. After adding 6 litres, water = 42 litres. Juice remains 48 litres. New ratio = 48:42 = 8:7 after dividing by 6, exactly matching the requirement.

Why Other Options Are Wrong:
38 litres: would make the new ratio too small compared to 8:7.52 or 56 litres: would make juice too large, pushing the ratio above 8:7.96 litres: typically comes from doubling without applying the ratio correctly.

Common Pitfalls:
Adding 6 litres to juice instead of to water.Using 4:3 and 8:7 as percentages rather than ratios.Forgetting to keep juice constant when only water is added.

Final Answer:
48 litres