Chain Rule
Chain Rule / Direct & Inverse Proportion
The chain rule links multiple quantities through direct and inverse proportion. Unitary method — finding the value of one unit first, then scaling — is the foundation of all chain rule problems. When more than two quantities are involved, classify each relationship as direct or inverse and set up a fraction chain.
Key Idea
Classify each relationship as Direct (same direction) or Inverse (opposite direction). Then multiply the ratio for Direct, invert and multiply for Inverse.
Core Formulas
Unitary method
Value of n units = (Value of 1 unit) × n
When value of one unit is known
Direct proportion
A₁/A₂ = B₁/B₂ → B₂ = B₁ × (A₂/A₁)
When quantities vary directly
Inverse proportion
A₁ × B₁ = A₂ × B₂ → B₂ = B₁ × (A₁/A₂)
When quantities vary inversely
Chain rule
Required = given × (D₁/D₂) × (I₂/I₁) × ...
For multi-variable proportion problems
Work-men-days
M₁ × D₁ × H₁ = M₂ × D₂ × H₂
When workers, days, and hours are all varying
Relevant Exams
2–3 questions per exam in SSC and RRB. Tests unitary method, direct/inverse proportion, and multi-variable chain. Common in work, speed, and cost problems.