Q. 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-1: 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?

a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.

b) The Question can be answered by using either Statement alone.

c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.

d) The Question cannot be answered even by using both the Statements together.

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

#### Question from UPSC Prelims 2024 CSAT

**Explanation : **

To determine who received the least amount among X, Y, and Z, let’s analyze the given statements:

**Statement I: **Given: X = 4/5(Y + Z)

Implication: The total amount distributed, T = X + Y + Z. Substituting from the statement:

T = 4/5(Y + Z) + Y + Z = 9/5(Y + Z)

Y + Z = 5/9T

X = 4/9T

Analysis: While we know X = 4/9T and Y + Z = 5/9T, we cannot determine the individual values of Y and Z. Without knowing how Y and Z are divided, we cannot conclusively identify who received the least.

### Statement II: Given: Y = 2/7(X + Z)

Implication:

Let X + Z = a. Then, Y = 2/7a and T = a + 2/7a = 9/7a

Y = 2/9T

X + Z = 7/9T

Analysis: Even though we know Y = 2/9T, without the individual values of X and Z, it’s unclear whether Y is the least or if X or Z could be lesser based on their distribution.

### Using Both Statements Together:

From Statement I: X = 4/9T

From Statement II: Y = 2/9T and X + Z = 7/9T

Substituting:

Y = 2/7(X + Z) = 2/7 × 7/9T = 2/9T

X = 4/9T

Z = 3/9T

Conclusion: The distribution ratios are X:Y:Z = 4:2:3. Clearly, Y receives the least amount.