Ratio, Proportion and Percentages Formulas and Tricks

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Ratio & Proportion

  • The equality of two ratios is called a proportion. If , we write and we say that a, b, c, d are in proportion. In a proportion, the first and fourth terms are known as extremes, while the second and third are known as means.

  • Mean proportion between a and b is

  • The compounded ratio of the ratios is

  • is a duplicate ratio of

  • is a sub-duplicate ration of

  • is a triplicate ratio of

  • is a sub-triplicate ratio of

  • If , then , which is called the Componendo.

  • If , which is called the dividendo

  • If , which is called the componendo & dividendo.

  • Variation: We say that x is directly proportional to y if for some constant k and we write,

  • Also, we say that x is inversely proportional to y for some constant k and we write

Ratios

  • If then for a positive quantity x,

  • If then for a positive quantity x,

Proportions

Percentage

  • To express x% as a fraction, we have

  • To express as a percent, we have

  • If ‘A’ is R% more than ‘B’, then ‘B’ is less than ‘A’ by

    OR

    If the price of a commodity increases by R%, then the reduction in consumption, not to increase the expenditure is

  • If ‘A’ is R% less than ‘B’, then ‘B’ is more than ‘A’ by

    OR

    If the price of a commodity decreases by R%, then the increase in consumption, not to increase the expenditure is

  • If the population of a town is ‘P’ in a year, then its population after ‘N’ years is

  • If the population of a town is ‘P’ in a year, then its population ‘N’ years ago is

Percentage Change

  • For two successive changes of and