Ratio and Proportion Concept — Complete Formula and Tricks

Q1. What is ratio and what does it mean?

A ratio is a comparison between two or more quantities of the same kind. It tells us how many times one quantity is greater or smaller than another. For example if A is 3 and B is 7 then the ratio of A to B is written as 3:7. In a ratio the first term is called the antecedent and the second term is called the consequent. Ratio is one of the most important topics in mathematics and is asked in every competitive exam.

Q2. What is the property of ratio?

The most important property of ratio is that if the numerator and denominator are multiplied or divided by the same number the value of the ratio does not change. For example x:y = xa:ya = x/a:y/a. This property is used extensively in simplifying ratio problems in competitive exams like CAT, SSC CGL and Bank PO.

Q3. What is proportion and how is it different from ratio?

When two ratios are equal the four quantities forming them are said to be in proportion. If a/b = c/d then a:b::c:d and these four quantities are in proportion. In a proportion a and d are called extremes and b and c are called means. The key property of proportion is that the product of extremes equals the product of means which means ad = bc. Ratio compares two quantities while proportion states that two ratios are equal.

Q4. What is the componendo rule in proportion?

The componendo rule states that if a/b = c/d then (a+b)/b = (c+d)/d. In simple terms componendo means adding the denominator to the numerator on both sides of the proportion. This rule is very useful in solving proportion problems quickly in competitive exams like CAT, SSC CGL, Bank PO and Railway RRB.

Q5. What is the dividendo rule in proportion?

The dividendo rule states that if a/b = c/d then (a-b)/b = (c-d)/d. In simple terms dividendo means subtracting the denominator from the numerator on both sides of the proportion. Dividendo is the opposite of componendo and both rules together form the componendo and dividendo rule which is one of the most powerful shortcuts in proportion.

Q6. What is the componendo and dividendo rule?

The componendo and dividendo rule states that if a/b = c/d then (a+b)/(a-b) = (c+d)/(c-d). This combined rule is one of the most frequently used shortcuts in competitive exam proportion problems. It allows you to solve complex proportion questions in just one step without performing lengthy calculations. This rule is asked in CAT, SSC CGL, SSC CHSL, Bank PO and all Railway exams.

Q7. What is continued proportion?

Three numbers a, b and c are said to be in continued proportion if a:b = b:c. In this case b is called the mean proportional between a and c. The key formula for continued proportion is b² = ac which means the square of the middle term equals the product of the first and third terms. Continued proportion is an important concept asked in CAT, SSC CGL and Bank PO exams.

Q8. Where can I practice ratio and proportion questions?

After understanding the concept you can practice on our Ratio and Proportion Exercise page which contains a large number of solved practice questions covering all types of ratio and proportion problems asked in competitive exams. You can also check our Percentage Concept and Mixture and Alligation Concept pages for related topics.