Properties of Ratios: CAT Quantitative Aptitude - Part 1

Ratio When comparing two quantities (of the same kind), sometimes it is necessary to find out the relationship that one quantity bears to another, this comparison is made by considering what multiple, part or parts, one quantity is of the other. This particular relationship between the two quantities (of the same kind) is called a ratio. As is evident by the explanation, a ratio does not have any units.

Example: 12 is 1/3 (one-third) of 36, or 36 is three times 12.

In this case we say “the ratio of 12 to 36 is equal to 1/3 ” or “the ratio of 36 to 12 is equal to 3”.  (Note: to find what multiple or part of a is of b, we divide a by b, hence the ratio a:b may be measured by the fraction a/b)

The numbers forming a ratio are called the terms of the ratio. The numerator of a ratio is called the antecedent and the denominator is called the consequent. In a ratio, the order of the terms is important as a:b is not same as b:a.

The ratio of two numbers is also expressed in hundredths. In this case, the hundredth part of a number is called per cent. For instance, the ratio 2:5 = 2/5=0.4  is equal to ‘40 hundredths’ or 40 per cent, and is written as 40%.

Properties of Ratios

1. Every ratio is an abstract quantity as it expresses the number of times one quantity contains another.

2. The value of ratio remains unaltered if the antecedent and the consequent are multiplied or divided by same quantity i.e.,

then, a/b= an/bn, and m/n = bm/bn

therefore a:b is '>, =, or ,' m:n accordingly as  an is '>, =, <' bm

Alternatively, if you have two ratios a/b and m/n

then, the cross-multiplication and comparison of quantity ‘an’ to ‘bm’

will indicate the relationship of > or < between a/b and m/n

If an>bm then a/b > m/n

If an<bm then a/b < m/n

4. The ratio of two fractions can be expressed as a ratio of two integers.

Thus, the ratio of fractions 3/4 and 5/4 can be measured by

5. When two or more than two ratios aremultiplied with each other, then it is called a compounded ratio.

That is for three ratios 2/3, 4/5, and 6/7

the compounded ratio =

6. When the ratio is compounded with itself, it is called as duplicate ratio, i.e.,

7.  A ratio is said to be ratio of greater inequality, of less inequality, or of equality, according as the antecedent is greater than, less than or equal to the consequent.

…This article is continued in ‘Properties of Ratios: CAT Quantitative Aptitude Part — 2’