CMA Foundation · Fundamentals of Business Mathematics and Statistics · Ratios, Variations and Proportions
A quantity y varies directly as x and inversely as the square of z. When x = 12 and z = 2, y = 9. Find y when x = 8 and z = 4.
The value of y is 1.5. Since y equals k times x divided by z squared, the first set gives k as 3. Substituting x = 8 and z = 4 yields 3 × 8 divided by 16, which equals 1.5.
- A1.5Correct
- B3
- C6
- D2.25
Explanation
y = kx/z², so 9 = k×12/4 = 3k and k = 3. Then y = 3×8/16 = 1.5. Check by ratios: 9 × (8/12) × (4/16) = 9 × 2/3 × 1/4 = 1.5. Using z instead of z² would give 3, a common mistake.
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