Inverse Proportion — O/L Mathematics

What must I remember about Inverse Proportion?

• Inverse proportion defines a relationship where an increase in one variable produces a proportional decrease in the other: product remains constant (x × y = k).
• Mathematical model: y ∝ (1 / x) or y = (k / x), where k is the constant of variation.
• Work-time and resource allocation: Total work done = (Number of workers) × (Number of days/hours) = constant person-days or machine-hours.
• Equating work across scenarios: W₁ × D₁ = W₂ × D₂ (assuming equal individual productivity rates).
• Graphical representation: The graph of y against x is a rectangular hyperbola asymptotic to both axes in the first quadrant.

Test yourself (1 minute)

1. Direct vs Inverse proportion trap

   In direct proportion y/x = constant (cross-multiply); in inverse proportion x × y = constant (multiply across rows).

2. Added workers problem

   If 6 workers take 10 days, total = 60 man-days; to finish in 4 days requires 60 / 4 = 15 workers; the ADDED workers needed = 15 - 6 = 9 workers.

3. Units in rates

   Ensure time units (hours, days, weeks) are consistent across all terms before equating products.

Practise Inverse Proportion questions today

Source: NIE G.C.E. (O/L) Mathematics Syllabus (Grade 10, Unit 9)

What should I study first?

What comes next?

Next in the syllabus

Where does Inverse Proportion fit in the syllabus?

Grade 10 · Term 1