Ratio, Proportion and Variation

Given that a/b=c/d, where a, b, c and d are non-zero real numbers, we can deduce other proportions by simple Algebra. These results are often referred to by the names mentioned along each of the properties obtained.

  • b/a=d/c (invertendo)
  • a/c=b/d (alternendo)
  • (a+b)/b=(c+d)/d (componendo)
  • (a-b)/b=(c-d)/d (dividendo)
  • a+b/a-b=c+d/c-d (componendo &dividendo)


Two quantities A and B are said to be varying with each other if there exists some relationship between A and B such that the change in A and B is uniform and guided by some rule.

Some typical examples of variation:

  • Area (A) of a circle = ΠR2, where R is the radius of the circle.

Area of a circle depends upon the value of the radius of a circle, or, in other words, we can say that the area of a circle varies as the square of the radius of a circle.

  • At a constant temperature, pressure is inversely proportional to the volume.
  • If the speed of any vehicle is constant, then the distance traversed is proportional to the time taken to cover the distance.


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