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?

Correct Option: (c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone

Let the amounts received by X, Y, and Z be x, y, and z respectively, and let T = x + y + z be the total amount. From Statement-I: x = (4/5)(y + z) ⇒ x = (4/5)(T - x) ⇒ 5x = 4T - 4x ⇒ 9x = 4T ⇒ x = (4/9)T. This gives X's share but does not provide individual shares of Y and Z to determine who received the least. Thus, Statement-I alone is insufficient. From Statement-II: y = (2/7)(x + z) ⇒ y = (2/7)(T - y) ⇒ 7y = 2T - 2y ⇒ 9y = 2T ⇒ y = (2/9)T. This gives Y's share but does not provide individual shares of X and Z. Thus, Statement-II alone is insufficient. Combining both statements: We have x = (4/9)T and y = (2/9)T. Since z = T - x - y, we get z = T - (4/9)T - (2/9)T = (3/9)T. Comparing the shares: y = (2/9)T, z = (3/9)T, and x = (4/9)T. Since T is positive, we see that (2/9)T < (3/9)T < (4/9)T, which means Y received the least amount. Both statements together are sufficient. Hence, the correct option is (c).