Chain Rule
Chain Rule / Direct & Inverse Proportion
Link multiple quantities through direct and inverse proportion by finding the value of one unit first, then scaling. SSC and RRB papers test 2\u20133 chain-rule questions per exam, often combining work, speed, and cost in a single problem. Classify each relationship as direct or inverse before setting up the 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
Divide total value by total units to get the per-unit rate, then multiply by the required number of units
Direct proportion
A₁/A₂ = B₁/B₂ → B₂ = B₁ × (A₂/A₁)
Apply when both quantities increase or decrease together \u2014 more workers produce more output, more hours cover more distance
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.