Percentage

Subject: Compulsory Maths

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Overview

Percent means parts per hundred or out of hundred. The symbol of a percent is %.
Percentage

Percent

source: igcseatmathematicsrealm.blogspot.com Fig: Percentage
source: igcseatmathematicsrealm.blogspot.com Fig: Percentage

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

source: nzmaths.co.nz Fig: Fraction or Demiacal into Percent
source: nzmaths.co.nz
Fig: 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,

Scholarships after +2 Abroad Studies Opportunities

\(\frac{2}{5}\) =\(\frac{2}{5}\) × 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

Things to remember
  • Percentage is a fraction written with a denominator 100.
  • For the conversion of a fraction or decimal into percent multiply it by 100 and put the symbol % to the product. 
  • For the conversion of percent into fraction or decimal, divide it by 100 and remove the % symbol. 
  • It includes every relationship which established among the people.
  • There can be more than one community in a society. Community smaller than society.
  • It is a network of social relationships which cannot see or touched.
  • common interests and common objectives are not necessary for society.
Videos for Percentage
How to work out percentages without a calculator!!
https://www.youtube.com/watch?v=JeVSmq1Nrpw
Questions and Answers

Solution:

Here,
\(\frac{3}{20}\) = \(\frac{3}{20}\) × 100% = 15%
∴ percentage of absentes = 15% 
Now,
the percentage of present students = 100% - 15% 
= 85 %

Solution: 

Here,
40% = \(\frac{40}{100}\) = \(\frac{2}{5}\) 
∴ Fractions of illiterate people = \(\frac{2}{5}\) 
Now,
the fraction of literate people = 1 - \(\frac{2}{5}\) = \(\frac{3}{5}\) 

Solution:

Here,
60 as the percentage of 80 = \(\frac{60}{80}\) × 100%
75%
So, he obtained 75% marks. 

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:

Here,
the total monthly income of the man = Rs 12,000
Expenditure on children's education = 20% of Rs 12,000 
= \(\frac{20}{100}\) × Rs 12,000
= Rs 2400

Expenditure on food = 25% of Rs 12,000 
= \(\frac{25}{100}\) × Rs 12,000 
= Rs 3,000

Expenditure on rent = 30% of Rs 12,000 
= \(\frac{30}{100}\) × Rs 12,000
= Rs 3,600

Solution:

Let his monthly income be Rs x.
Here,
His saving percentage = 100% - 65% 
= 35%
Now,
or, 35% of x = Rs 2800 
or, \(\frac{35}{100}\) × x = Rs 2800 
or, \(\frac{7x}{20}\) = Rs 2800
or, x = \(\frac{20 \; × \; Rs 2800}{7}\) 
or, x = Rs 8000
∴ His monthly income = Rs 8000
Now, 
His monthly income = Rs 8000 - Rs 2800 
Rs 5200
So, he spends Rs 5200 every month

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.

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