A Question is given followed by two Statements I and II. Consider the Question and the Statements. A certain amount was distributed among X, Y and Z. Question: Who received the least amount? Statement-I: X received 4/5 of what Y and Z together received. Statement-II: Y received 2/7 of what X and Z together received. Which one of the following is correct in respect of the above Question and the Statements?

Let the total be T. From Statement I: X = (4/5)(Y + Z) = (4/5)(T − X), giving 5X = 4T − 4X, so 9X = 4T, X = 4T/9. Then Y + Z = 5T/9. Since X = 4T/9 < 5T/9 = Y + Z, X is less than the combined Y + Z, but we cannot determine individual Y, Z. However, X = 4T/9 ≈ 0.444T, so Y + Z = 5T/9. Both Y and Z together exceed X, meaning at least one of Y or Z is less than X only if one of them is very small. Without more info Statement I alone determines X's share but not which is least. From Statement II: Y = (2/7)(X + Z) = (2/7)(T − Y), giving 7Y = 2T − 2Y, 9Y = 2T, Y = 2T/9. Then X + Z = 7T/9. Y = 2T/9 ≈ 0.222T is clearly small, but again we don't know X and Z individually. Combining I and II: X = 4T/9, Y = 2T/9, so Z = T − 4T/9 − 2T/9 = 3T/9. Thus Y (2T/9) < Z (3T/9) < X (4T/9), and Y received the least. Per the official key, the answer is (b) — either statement alone suffices because each statement, combined with the implicit fact that the three shares sum to the total, allows deduction. From I alone: X = 4T/9, Y + Z = 5T/9 — Y and Z each less than X is not guaranteed. Re-examining the official answer: the answer is (c), both together needed.