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Ratio and Proportion

Ratio and Proportion​

Core rules:

If A:B = x:y, then A = kx and B = ky
a/b = c/d => ad = bc
If A:B = x:y and B:C = p:q, make B common

Useful properties:

a:b = c:d
=> (a+b):(a-b) = (c+d):(c-d)
=> a/(a+b) = c/(c+d)

Variation:

A directly varies with B => A/B = constant
A inversely varies with B => A*B = constant
A varies directly with B and inversely with C => A = kB/C

Speed tricks:

  • Convert shares into kx, ky, kz first.
  • For ratio changes after adding/removing, use equations only on the changing part.
  • If total is known, add ratio parts and divide total by sum of parts.
  • In partnership, profit ratio = capital * time.