Subject: Compulsory Maths

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

- 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.

\(\frac{3}{20}\) of the number of students of a class were absent on a day. Find the percentage of present students.

Solution:

Here,

\(\frac{3}{20}\) = \(\frac{3}{20}\) × 100% = 15%

∴ percentage of absentes = 15%

Now,

the percentage of present students = 100% - 15%

= 85 %

If 40% of the people in a village are illiterate, what fraction of the people are literate?

Solution:

Here,

40% = \(\frac{40}{100}\) = \(\frac{2}{5}\)

∴ Fractions of illiterate people = \(\frac{2}{5}\)

Now,

the fraction of literate people = 1 - \(\frac{2}{5}\) = \(\frac{3}{5}\)

Sameer obtained 60 marks out of 80 full marks ion Maths. Express his marks in percentage.

Solution:

Here,

60 as the percentage of 80 = \(\frac{60}{80}\) × 100%

75%

So, he obtained 75% marks.

The rate of a price of petrol is increased from Rs 50 per liter to Rs 55 per liter. Find the percentage increase in the price.

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%

The monthly income of a man is Rs 12,000. He spends 20% of hiss income on his children's education, 25% on food, 30% on house rent and he save the rest in a bank. Find his expenditure in each item.

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

Father spends 65% of his monthly income to run the family and the rest he saves in a bank. If he saves Rs 2800 in the bank, how much does he spend every month?

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

There are 225 boys in a school which is 75% of the total number of students. Find the number of girls in the school.

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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