Water added to adjust alcohol mixture – UGC NET Question

Initially, alcohol = (5/12) × 72 = 30 litres and water = (7/12) × 72 = 42 litres. Let x litres of water be added. Alcohol remains 30 litres, water becomes 42 + x and the new ratio is 30:(42 + x) = 5:9. Cross-multiplying gives 30 × 9 = 5(42 + x), so 270 = 210 + 5x, which leads to 5x = 60 and x = 12. Thus, 12 litres of water must be added.

Option A:
Option A, 9 litres, gives water = 51 litres and alcohol = 30 litres, yielding a ratio 30:51 which simplifies to 10:17, not 5:9. Hence, 9 litres is insufficient to reach the required proportion of water to alcohol.

Option B:
Option B, 10 litres, leads to water = 52 litres and a ratio 30:52, which reduces to 15:26. This is still not 5:9, indicating that 10 litres does not adjust the mixture to the desired composition.

Option C:
Option C, 11 litres, produces water = 53 litres and a ratio 30:53 which does not simplify to 5:9. Therefore, it also fails to create the target ratio between alcohol and water.

Option D:
Option D is correct because with water increased to 54 litres, the ratio becomes 30:54, which simplifies to 5:9 when both terms are divided by 6. This exactly matches the condition specified in the problem.