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Percent means parts per hundred or out of hundred. The symbol of a percent is %.
For example, 25% means 25 per 100 or, \(\frac{25}{100}\)
Percentage is a fraction written with a denominator 100.
Conversion of fraction or decimal into percent
For the conversion of a fraction or decimal into percent multiply it by 100 and put the symbol % to the product. For example,
\(\frac{2}{5}\) =\(\frac{2}{5}\) × 100 % = 40 %
0.3 = 0.3× 100 % = 30 %
Conversion of percent into fraction or decimal
For the conversion of percent into fraction or decimal, divide it by 100 and remove the % symbol. For example,
20% =\(\frac{20}{100}\) =\(\frac{1}{5}\)
32% =\(\frac{32}{100}\) = 0.32
To express a given quantity as the percent of whole quantity
For the expression of the given quantity as the fraction of the whole quantity, then multiply the fraction by 100%. For examples,
20 as the percent of 80 =\(\frac{20}{80}\) × 100 = 25%
To find the value of given percent of a quantity
If this case is given, then multiply the quantity by the given percent. Then, convert the percent into a fraction and simplify. For example,
25% of Rs.250 = 25%× 250 =\(\frac{25}{100}\)× 250 = Rs. 62.5 ans.
To find a quantity whose value of certain percent is given
If this case is given, we can suppose the whole quantity by a variable such as x. Then we can form an equation and by solving the equation we can find the value of x. For example,
If 20% of a sum is Rs. 80. Find the sum
Here, Let the sum be Rs.x
Now, 20% of x = Rs.80
or, \(\frac{20}{100}\)× x = Rs. 80
or, \(\frac{x}{5}\) = Rs.80
or, x =Rs. 80 × 5 = Rs.400
Solution:
Here,
the initial rate of a price = Rs 50 per liter
The new rate of a price = rs 55 per liter
∴ Increment in the rate price = Rs 55 - Rs 50 = rs 5
Now,
the increment percentage = \(\frac{Increment \; price}{Initial \; price}\) × 100%
= \(\frac{Rs \; 5}{Rs \; 50}\) × 100%
= 10%
So, the rate of a price of petrol is increased by 10%
Solution:
Let, the total number of students in the school be x.
Here,
or, 75% of x = 225
or, \(\frac{75}{100}\) × x = 225
or, \(\frac{3x}{4}\) = 225
or, x = \(\frac{4 × 225}{3}\)
or, x = 300
So, the total number of students in the school is 300,
Again,
Number of girls = 300 - 225
So, there are 75 girls in the school.
Sameer obtained 60 marks out of 80 full marks in Maths. Express his marks in percentage.
Express (frac{7}{20}) in percentage.
Express 0.48 in percentage.
Express 56% in decimal.
Express the Rs 36 as a percentage of Rs 720.
Find the value of 75% of 60 full marks.
Find the quantity whose 10% is Rs 160.
(frac{3}{4}) of the total number of students in a school are boys. Find the percentage of boys.
There are 48 students in a class. If 36 of them are boys, find the percentage of boys.
52% of the total students in a school are girls. If there are 130 girls, find the total number of students in a school.
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