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