2021 · Q85
Consider the following statements:
- 1If x is directly proportional to z and y is directly proportional to z, then (x² − y²) is directly proportional to z².
- 2If x is inversely proportional to z and y is inversely proportional to z, then (xy) is inversely proportional to z².
Which of the above statements is/are correct?
Elementary MathematicsRatio and Proportion
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
Statement 1: x = mz, y = nz gives x² − y² = (m²−n²)z² ∝ z² — true. Statement 2: x = a/z, y = b/z gives xy = ab/z² ∝ 1/z² — true. Both statements are correct. Hence option C.