Q65. A Question is given followed by two Statements I and
II. Consider the Questions 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 amount distributed be T = X + Y + Z. **Statement I: X received 4/5 of what Y and Z together received.** X = (4/5)(Y + Z) Since Y + Z = T - X, we have X = (4/5)(T - X) 5X = 4T - 4X => 9X = 4T => X = 4T/9.

This statement tells us X's share relative to the total, but we cannot compare X, Y, and Z individually. So, Statement I alone is insufficient. **Statement II: Y received 2/7 of what X and Z together received.** Y = (2/7)(X + Z) Since X + Z = T - Y, we have Y = (2/7)(T - Y) 7Y = 2T - 2Y => 9Y = 2T => Y = 2T/9.

This statement tells us Y's share relative to the total, but we cannot compare X, Y, and Z individually. So, Statement II alone is insufficient. **Combining Statement I and Statement II:** From Statement I, X = 4T/9.

From Statement II, Y = 2T/9. Since X + Y + Z = T, we can find Z: (4T/9) + (2T/9) + Z = T 6T/9 + Z = T 2T/3 + Z = T Z = T - 2T/3 = T/3 = 3T/9. Now we have the shares: X = 4T/9 Y = 2T/9 Z = 3T/9 Comparing these values, Y (2T/9) received the least amount.

Thus, both statements together are sufficient to answer the question. This question tests data sufficiency and algebraic reasoning with ratios.