Which information is/are sufficient to answer the questions asked? A vessel contains a mixture of two milk A and B. How much of the milk ‘A’ was there in the vessel? I. 9 litres of mixture is replaced by 9 litres of milk B. II. The initial ratio of milk A and B in the mixture was 7 : 5. III. The new ratio of milk A and B in the mixture is 7 : 9.

Let initial quantities be 7x of milk A and 5x of milk B, so total = 12x litres. Statement III alone is insufficient without knowing total quantity. Statement II gives the ratio but not the total. Statement I: When 9 litres of mixture is removed, it contains A and B in 7:5 ratio, so 9 × 7/12 = 5.25 litres of A and 9 × 5/12 = 3.75 litres of B are removed. Remaining: A = 7x - 5.25, B = 5x - 3.75. After adding 9 litres of B: A = 7x - 5.25, B = 5x - 3.75 + 9 = 5x + 5.25. New ratio (A:B) = 7:9, so (7x - 5.25)/(5x + 5.25) = 7/9. Solving: 63x - 47.25 = 35x + 36.75, so 28x = 84, x = 3. Initial milk A = 7x = 21 litres. All three statements together are necessary and sufficient.