# 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,

## 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