Ratio and Proportion Made Easy: Formulas, Tricks, and Shortcuts

Ratio and Proportion is a high-weightage topic in quantitative aptitude for SSC, Banking, Railway, and other competitive exams. Many questions in percentage, profit and loss, time and work, and mixtures are directly based on ratio and proportion concepts. Understanding the formulas, properties, and shortcut tricks of ratio and proportion can help you solve questions quickly and accurately in exams.

Ratio & Proportion Quiz 1

Ratio & Proportion Quiz 2

Ratio:

The ratio of two quantities a and b in the same units, is the fraction   and we write it as a : b.

In the ratio a : b, we call a as the first term or antecedent and b, the second term or consequent.

The ratio 5 : 9 means:

 

$$\frac{5}{\mathrm{9<span\; style="font-family:\; Georgia,\; \text{'}Times\; New\; Roman\text{'},\; \text{'}Bitstream\; Charter\text{'},\; Times,\; serif;"><span\; style="color:\; \#000000;"></span></span>}}$$

 

• Antecedent = 5

• Consequent = 9

Rule: The multiplication or division of each term of a ratio by the same non-zero number does not affect the ratio.

e.g. 4:5 = 8 : 10 = 12 : 15. Also, 4 : 6 = 2 : 3.

Proportion:

The equality of two ratios is called proportion.

If a: b = c : d, we write a : b:: c : d, and we say that a, b, c, d are in proportion.

Here, a and d are called extremes, while b and c are called mean terms.

Product of means = Product of extremes.

Thus, a : b :: c : d   (b x c) = (a x d).

Fourth Proportional: If a: b = c : d, then d is called the fourth proportional to a, b, c.

Third Proportional: a: b = c : d, then c is called the third proportion to a and b.

Mean Proportional: Mean proportional between a and b is ab.

Comparison of Ratios: We say that (a: b) > (c : d)   

If:

 

$$\frac{a}{b}>\frac{c}{d}$$

 

Then: $$a:b>c:d$$

Compounded Ratio: The compounded ratio of the ratios: (a : b), (c : d), (e : f) is (ace : bdf).

Duplicate Ratios:

Duplicate ratio of (a : b) is (a² : b²).

Sub-duplicate ratio of (a : b) is (  :  ).

Triplicate ratio of (a : b) is (a³ : b³).

Sub-triplicate ratio of (a : b) is (a^1/3 : b^1/3).

If	a	=	c	, then	a + b	=	c + d	.     [componendo and dividendo]
	b		d		a – b		c – d

Variations:

We say that x is directly proportional to y, if x = ky for some constant k and we write, x   y.

We say that x is inversely proportional to y, if xy = k for some constant k and

we write x	1	.
	y

To score well in quantitative aptitude, you must master Ratio and Proportion formulas and concepts. Focus on product of means and extremes, mean proportional, and variations, as these are frequently tested in exams. Regular practice and quick revision of ratio and proportion shortcuts will improve both speed and accuracy.

Ratio and Proportion FAQ

Q. How many questions come from Ratio and Proportion in competitive exams?

Ans. In most SSC, Banking, and Railway exams, 1–3 direct questions and 2–4 indirect questions are based on Ratio and Proportion.

Q. What are the most important formulas of Ratio and Proportion for exams?

Ans. Important formulas include a : b = c : d, product of means equals product of extremes (b × c = a × d), mean proportional √(ab), direct proportion x = ky, and inverse proportion xy = k.

Q. Which topics are connected to Ratio and Proportion?

Ans. Ratio and Proportion is connected to percentage, profit and loss, mixture and alligation, time and work, and partnership.