Mixture replacement ratio change – UGC NET Question

Let the total quantity be T litres. Initially, milk = (5/8)T and water = (3/8)T. When 16 litres are removed from a well-mixed solution, milk removed = (5/8) × 16 = 10 litres and water removed = 6 litres. So the remaining milk is (5/8)T − 10 and the remaining water is (3/8)T − 6. After adding 16 litres of water, water becomes (3/8)T + 10. The new ratio is [(5/8)T − 10] : [(3/8)T + 10] = 5:4. Solving this proportion yields T = 144 litres.

Option A:
Option A, 96 litres, would give initial milk 60 litres and water 36 litres. After removing 16 litres and adding 16 litres of water, the final milk and water quantities would not reduce to the ratio 5:4; a detailed check shows the ratio differs from 5:4. Hence 96 litres does not satisfy the given condition.

Option B:
Option B, 128 litres, leads to initial milk 80 litres and water 48 litres. Following the same removal and replacement process, the resulting milk and water do not maintain a 5:4 ratio. The mathematical equation for the final ratio fails when T = 128, so this value is incorrect.

Option C:
Option C is correct because with T = 144 we get initial milk 90 litres and water 54 litres. Removing 16 litres removes 10 litres of milk and 6 litres of water, leaving 80 litres of milk and 48 litres of water. Adding 16 litres of water gives 80 litres of milk and 64 litres of water, giving 80:64 = 5:4. This exactly matches the new ratio stated.

Option D:
Option D, 160 litres, would create larger starting volumes but the same removal and replacement would not lead to a 5:4 ratio. Solving the final ratio equation with T = 160 gives a contradiction, meaning that this total volume cannot produce the described outcome.