Uses of Ratio and Proportion

Quantitative Aptitiude (CLAT) Ratio, Proportion

WHAT IS RATIO:-

Ratio is a mathematical term used to compare two similar quantities expressed in the same units. The ratio of two terms ‘x’ and ‘y’ is denoted by

x : y. In ratio x : y , we can say that x as the first term or antecedent and y, the second term or consequent.

In general, the ratio of a number x to a number y is defined as the quotient of the numbers x and y i.e. x/y.

Example: The ratio of 25 km to 100 km is 25:100 or 25/100, which is 1:4 or 1/4 .

Note that fractions and ratios are same; the only difference is that ratio is a unit less quantity while fraction is not.

What is a Proportion?

Proportion is an equality between two ratios.

i.e. a: b :: c : d

Where a, b, c, and d are said to be in proportion.
a, b, c and d are referred to as first, mean, third and fourth proportional respectively.

a and d are called Extreme Proportion and b and c are called Mean Proportion.

As we know a: b can be written as a/b

we can write a/b = c/d

As the terms are equal we cross multiply,

ax d = b x c

The product of extremes should be equal to the product of means.

Types of proportions

Fourth proportion = When a:b::c:d, then d is called as fourth proportion of a,b and c

Mean proportion = When a:b::b:c, then b is called as mean or second proportion of a and c

Third proportion = When a:b::b:c, then c is called as third proportion of a and b

First proportion = When a:b::b:c, then a is called as first proportion of b and c

Reciprocal ratio: The reciprocal ratio of the ratio m : n (m ≠ 0, n ≠ 0) is the ratio 1/m : 1/n

For any ratio x : y, where x, y ≠ 0, its reciprocal ratio = 1/x : 1/y = y : x

Similarly, we can say if the antecedent and consequent of a ratio be interchanged, the changed ratio is called the inverse ratio of the previous ratio.

For example:

Reciprocal ratio of 7 : 13 = 1/7 : 1/13 = 13 : 7.

5 : 7 is the inverse ratio of 7 : 5

Same difference between two ratios or numbers:- When two number are increased or decreased by same value then the difference between both numbers as wll as their ratios is same.