Questions on Proportions are very common in the CAT Exam in the quantitative aptitude section. Candidates appearing for the CAT exam generally get word problems in which concept of ‘proportion’ is asked to test the aptitude.

Some examples are illustrated for the candidates to help them prepare for this topic from CAT exam point of view. Initially, you will see concepts pertaining to ‘proportion’ and thereafter examples related to it. Undoubtedly, every year CAT exam carries 2-3 questions from this topic in either quantitative aptitude section or logical reasoning & data interpretation section in various forms. Take a look at the exercise provided below and get ready to appear in the CAT exam with flying colours of success.

**Proportion**

An equality of two ratios is called a proportion. In another way, four quantities are said to be in proportion if the ratio of the first to the second quantity is equal to the ratio of the third to the fourth quantity.

Example:

If a/b = c/d or a : b = c : d, then we say that a, b, c, and d are in proportions and written as it is read as ‘a is to b as c is to d’ and where the symbol ‘::’ indicates proportion.

The terms ‘a and d’ are called the *extremes*, and the terms ‘b and c’ the* means*. In a proportion, the order of terms is important as 3: 10 :: 15 : 50 are in proportion, but 3: 10 :: 50 : 15 are in a different proportion.**Properties of Proportions****1.** The product of extremes is equal to the product of the means.

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

then, a×d=b×c

**2. **If a, b, c, d… are such that a : b = b : c = c : d …then these numbers a, b, c, d… are said to be in continued proportion or simply in proportion.

If three quantities a, b, c are in *continued proportion*, then

a : b = b : c

therefore ac = b^{2 }

In this case, b is said to be a **mean proportional** between a and c; and c is said to be a third proportional to a and b.

Note:If three quantities a, b, and c are proportional, the first is to the third as the duplicate ratio of the first to the second.

i.e., a : b :: b : c

then a : c = a^{2} : b^{2 }

**3.** If four quantities a, b, c, d form a proportion, many other proportions may be deduced by the properties of fractions. As —**i.** If a : b = c : d, then b : a = d : c and is called *Invertendo*

**ii.** If a : b = c : d, then a : c = b : d and is called *Alternendo***iii.** If a : b = c : d, then a + b : b = c + d : d and is called *Componendo*

**iv.** If a : b = c : d, then a – b : b = c – d : d and is called *Dividendo*

**v.** If a : b = c : d, then a + b : a – b = c + d : c – d and is called Componendo and *Dividendo*

**Solved Examples**

**Problem 1: **

What is the least possible number which must be subtracted from 7, 9 and 12 so that the resulting numbers are in continued proportion?

[1] 1

[2] 2

[3] 3

[4] 4**Solution: **

Let the number be x.

Then,(7-x) : (9-x) ::(9-x)(12-x)

Hence, option [3] is the answer.

Ratios and Proportion is a topic which never goes out of syllabus and that is why questions based on this topic are asked over and over again in various entrance examinations.

**Also Practise**

** MBA Quantitative Aptitude Questions & Answers – Ratio and Proportion Set-I**