Ratio and Proportion: Formulas and Shortcuts

Ratio and Proportion is one of the easiest concepts from competitive exam perspective. Questions from this concept are mostly asked in conjunction with other concepts like ‘Mixtures & Alligations’.

Learn the formulas and shortcuts of Mixture and Alligation

RATIOS

Ratio of two quantities a and b in same units is the fraction of the two quantitiesand is written as

Where a is called as the antecedent and b is called as the consequent.

COMPARISON OF RATIOS

Ratios can be compared. When it is said that a: b > c: d, then it means,

DIFFERENT TYPES OF RATIOS

PROPERTIES OF RATIO

If both antecedent and consequent are multiplied or divided by the same number the ratio remains unchanged.

Ratio of two fractions can be expressed in fraction as follows:

If a: b :: c: d= n, where n is a constant then,

Ifa/A, b/B, c/C are unequal fractions then their ratio

lies between the lowest and highest fraction.

If two different numbers (c and d) are to be added to the antecedent (a) and consequent (b), then it must be satisfy the following condition:

For example, if and if 3 and 5 are to be added to the numerator and denominator respectively, then it follows as:

where

PROPORTION

Proportion is the equality of two fractions, that is a: b = c: d. This can be represented as a: b :: c: d,

Where a and d are called extremes and b and c are called the mean of the ratio.

FOURTH, THIRD AND MEAN PROPORTIONS

In a : b :: c : d, d is the fourth proportion of a, b and c; and c is the third proportion of a and b.

The mean proportion of a and b is 

DIFFERENT FORMS OF PROPORTION

PROPERTIES OF PROPORTION

Product of extremes is equal to the product of means.

If a: b :: b: c, then

If three quantities are in proportion as in a: b :: b: c, then,

where b is the mean proportion to a and b. c is the third proportion to a and b.

If three quantities are in proportion as in a: b :: b: c, then,