2023 · Q95
Question: What is the ratio x : y : z equal to if x, y, z ≠ 0?
Statement I(x + z)/y = z/x.
Statement II(z − y)/x = x/z. Mark option (a) if the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone. Mark option (b) if the question can be answered by using either statement alone. Mark option (c) if the question can be answered by using both the statements together, but cannot be answered using either statement alone. Mark option (d) if the question cannot be answered even by using both the statements together.
Elementary MathematicsRatio and Proportion
- AThe question can be answered by using one of the statements alone, but cannot be answered using the other statement alone
- BThe question can be answered by using either statement alone
- CThe question can be answered by using both the statements together, but cannot be answered using either statement alone
- DThe question cannot be answered even by using both the statements together
Explanation
St.I: x^2+xz=yz; St.II: z^2-yz=x^2; each leaves a free parameter. Together: z(x+z-2y)=0 gives x+z=2y, then 3xy=2y^2, y=3x/2, z=2x: ratio 2:3:4 uniquely. Both needed. Option (c). Key disputed: verify against the official UPSC key.