CMA Foundation · Fundamentals of Business Mathematics and Statistics · Ratios, Variations and Proportions
The quantity y varies directly as x and inversely as the square of z. When x = 6 and z = 2, y = 9. What is y when x = 8 and z = 4?
The value of y is 3. Writing y = kx/z², the first set of values gives k = 9×4/6 = 6. Substituting x = 8 and z = 4 gives y = 6×8/16 = 3.
- A3Correct
- B6
- C4
- D2
Explanation
y = kx/z². From 9 = k×6/4, k = 6. Then y = 6×8/16 = 3. Check via ratio: (8/6)×(4/16) = 1/3, and 9 × 1/3 = 3. Option 6 comes from treating z as inversely, not squared, giving 9×(4/3)×(1/2)=6.
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