Ratios & Proportions

Ratio is the relation that exists between two numbers or two quantities of the same units. Ifa andb are such quantities, then their ratio is written asa : bora/b. For example the ratio of 5 to 15 will be expressed as

5 : 15 or or 1 : 3. Herea is called the antecedent and b is called the consequent.

The equality of two ratios is called proportion. For example 3 : 5 = 6 : 10.
Here we say that 3, 5, 6 and 10 are in proportion and write as follows:
3 : 5 :: 6 : 10; Here 3, 5, 6, 10 are respectively known as first, second, third and fourth terms.

The first and fourth terms are known as extreme terms.
The second and third terms are known as mean terms.
If four quantities are in proportion, then Product of means=Product of extremes
If a: x:: x: bthen x is called the mean proportion between a and b. Clearly, x2= ab
Thus the mean proportion between any two numbers is equal to the square root of their products.


Example: If 3 : 21 :: x : 63, find the value of x.

Product of means = Product of extremes ? 21 × x = 3 × 63 or x = = 9

Example Find the fourth proportional of 1, 2, 3.

Let the fourth proportional be x; ? 1 : 3 :: 2 : x or x = 6.

Example: Find the third proportional of 6 and 30.

Let the third proportional be x
Then 6 : 30 :: 30 : x or x = = 150

Example: Find the mean proportional to .9 and 4.9.

Let the mean proportional be x.

⚡ Recently practiced quizzes in this class

Quantitative Aptitude Practice Test: HCF & LCM Ratio and Proportion Quantitative Aptitude Practice Test: Time and Distance Quantitative Aptitude Practice Test: Simplification And Simplification Word Problems Time - Speed and Distance Quantitative Aptitude Practice Test: Average Quantitative Aptitude Practice Test: Ratio and Proportion Quantitative Aptitude Practice Test: Power Cycle Quantitative Aptitude Practice Test: Real Numbers and BODMAS Simplification Quantitative Aptitude Practice Test: Percentage