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Ratio and Percentages

Comparing Quantities I - Concepts

Ratio and Percentages

Using OF Operator in Percentages

Express the Fraction as Percentage

Express Decimal as Percentage

Express as Percentage

Percentage Change

Successive Percentage Change

Percentage Increase or Decrease Using Multiplier

Percetage Increase or Decrease

Unitary Method In Percentages

Class - 8th Foundation NTSE Subjects

Concept Explanation

Ratio and Percentages

Ratio and Percentage:

Ratio: The ratio of two quantities 'a' and 'b' of the same kind and in the same units is a fraction $large frac{a}{b}$ which shows that how many times one quantity is of the other and is written as a : b and is read as 'a is to b' where b ≠ 0.

Terms of the ratio: In the ratio a : b, the quantities a and b are called terms of the ratio. Here, 'a' is called the first term or the antecedent and `b' is called the second term or consequent. In the ratio 5 : 9, 5 is called the antecedent and 9 is called the consequent.

Properties of ratio: If the first term and the second term of a ratio are multiplied / divided by the same non-zero number, the ratio does not change.

$frac{a}{b}=frac{xa}{xb},; where ;(x neq 0) So,; a : b =; xa : xb$

$frac{a}{b}=frac{frac{a}{x}}{frac{x}{b}},; where ;(x neq 0) So,; a : b =; frac{a}{x} :frac{b}{x}$

Ratio in the simplest form: A ratio a : b is said to be in the simplest form if a and b have no common factor other than 1.

Example: Express 15 : 10 in the simplest form.

Solution: $frac{15}{10}=frac{15div 5}{10div 5}= frac{3}{2}$

In this we cancelled the common factor 5. Thus, we have expressed the ratio

$frac{15}{10}; in; the; simplest; form,; i.e.,frac{3}{2}$

and the terms 3 and 2 have common factor only 1.

Percentages: The word percent means per hundred.

Conversion of Ratio into Percent: $x:y=frac{x}{y}= left [ frac{x}{y};X ;100 right ] %$

Example: Convert 3:4 into percent

Solution: $3:4=frac{3}{4}= left [ frac{3}{4};X ;100 right ] %=25%$

Ratio and Percentage: To express a ratio as percentage we add both the ratios. Then we divide the ratio with the sum of ratios and multiply it with 100.

Example: Express 2:3 as percentage

Solution: First we find the sum of ratios: 2+3 = 5

The divide the first ratio i.e. 2 with 5 and multiply with 100.

$dpi{100} frac{2}{5}; X ;100 =; 40%$

The divide the second ratio i.e. 3 with 5 and multiply with 100

$frac{3}{5} ;X ;100 = ;60%$

Or The second ratio can also be found as 100% - 40% = 60%

Hence, we can express each part of ratio x:y as percentage

$=frac{x}{x+y};X; 100,; frac{y}{x+y};X ;100$

Sample Questions

(More Questions for each concept available in Login)

Question : 1

Convert 10:40 ratio to percent.
A. 75%	B. 80%	C. 25%	D. 40%
Right Option : C
View Explanation

Question : 2

A ratio is a comparison by division of two quantities with the ________________ unit.
A. Same	B. Different	C. Unknown	D. Metre
Right Option : A
View Explanation