CMA Foundation · Fundamentals of Business Mathematics and Statistics · Ratios, Variations and Proportions
The monthly electricity charge of a factory varies jointly with the number of machines and the hours of operation per machine. With 8 machines running 10 hours, the charge is ₹16,000. What is the charge with 12 machines running 7 hours?
The charge is ₹16,800. With joint variation the constant is 16,000 divided by 80 machine-hours, giving ₹200. The new usage is 12 × 7 = 84 machine-hours, so the charge is 200 × 84 = ₹16,800.
- A₹16,800Correct
- B₹18,000
- C₹19,200
- D₹21,000
Explanation
Charge = k × machines × hours. k = 16,000/(8×10) = 200. New charge = 200 × 12 × 7 = ₹16,800. Option ₹19,200 comes from varying only with machines (1.5 × 16,000 = 24,000 is not it) and ignoring the change properly; the joint ratio is (12×7)/(8×10) = 1.05.
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