Note on Percentage

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A percentage is a number or ratio which shows a fraction of 100. It is often denoted using the percentage sign " % ".

For example, 65 % is equal to \(\frac{60}{100}\) or 0.655.

Example:

60% of 2000

= \(\frac{60}{100}\) x Rs 2000

= Rs 1200

Percentage can be determined by the following ways:

Commission

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The commission is meant to motivate sales person to sell more. Sales commission are paid to employee or companies that sell goods in stores or by calling on customers.

A commission is generally a percentage of the sales price of an item.

Example:

If a sales person receives 15% commission on his sales and sells Rs 5000 worth of merchandise, he would earn 15% of Rs 5000

\(\frac{15}{100}\)x Rs 5000

= Rs 750 ( commission)

Discount

There is discount in the sale or purchase of goods or services .The store will often sell items for a discounted sales price.

Example:

An item that originally cost Rs 500 may be discounted by 20% of Rs 500.

20% of Rs 500 = \(\frac{20}{100}\) x Rs 500

= Rs 100

Subtract the discount amount from the original price to finds the sales price.

Sales price = Original price - discount

= Rs 500 - Rs 100

= Rs 400

Income Tax

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.

Income Tax is levied on the income of individuals by the government of the country. The Government will not charge tax in all the income it will charge above certain criteria.

Example:

Jos Magar's monthly salary is Rs 30,000. If 10% income tax is levied on the amount of Rs 100,000, how much income tax will he pay in a year?

Solution:

Monthly income = Rs 30,000

Yearly income = Rs 30,000 x 12 = Rs 360,000

Taxable income = Rs 360,000 - Rs100,000 = Rs 260,000

Income Tax = 10% of Rs 260,000 = \(\frac{10}{100}\) x Rs 260,000 = Rs 26,000

Value Added Tax (VAT)

Value added tax (VAT) is added to the price of most things we buy.

Example:

A car costs Rs 40,00,000 before VAT. Work out the cost of the VAT if it is charged at 25%.

Solution:

Cost of the car before Tax = Rs 40,00,000

VAT Rate = 25%

Now, VAT amount = 25% of Rs 40,00,000

= \(\frac{25}{100}\) x Rs 40,00,000

= Rs 10,00,000

Percent Change

Have a look at this formula.

Percent Change = \(\frac{Amount\;of\;change}{Original\;Value}\) x 100

Example:

The price of rice is increased from Rs 100 to Rs 120 per kg. By how much percentage has the price increased?

Solution:

Original Price = Rs 100

New Price = Rs 120

Percentage increase = \(\frac{Amount\;of\;change}{Original\;Value}\) x 100

=\(\frac{20} {100}\) x 100

= 20%

 

  • The percentage is often denoted by the percentage sign "%".
  • It is the ratio or number as a fraction of 100.
  • The percentage is calculated by dividing the given percentage by 100 and multiplying the price.
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Very Short Questions

Solution:

Given information:

Price of the Jacket = Rs 1250

Price after discount = Rs 1100

Actual discount = Rs 1250 - RS 1100 = Rs 150

Discount percentage = \(\frac{discount amount}{total amount}\) \(\times\) 100%

= \(\frac{150}{1250}\) \(\times\) 100%

= 12 %

Solution:

Given information,

Price of a cap = Rs 350

Price of cap after discount = Rs 315

Actual Discount = Rs 350 - Rs 315 = Rs 35

∴ Discount Percentage = \(\frac{Discount Amount}{Actual Price }\) × 100

= \(\frac{35}{350}\)× 100

= 10%

Solution:

Given information,

Let, the marked price of the Television be x.

So, 13% discount = Rs 3,000

or, x × \(\frac{13}{100}\) = Rs 3,000

or, x = \(\frac{3,000× 100}{13}\)

or, x = Rs 23,076.92

∴ Marked price of Television = Rs 23,076.92

Solution:

Given information,

Monthly Income = Rs 25,000

Yearly income = Rs 25,000× 12 = Rs 3,00,000

Taxable Income = Rs 3,00,000 - Rs 2,00,000 = Rs 1,00,000

Income Tax = 15% of Rs 1,00,000

= \(\frac{15}{100}\)× Rs 1,00,000

= Rs 15,000

\(\therefore\) He pays Rs 15,000 income tax in a year.

Solution:

Given information,

Cost of a furniture before VAT = Rs 20,00,000

VAT rate = 20%

Now,

VAT amount = 20% of Rs 20,00,000

= \(\frac{20}{100}\)× Rs 20,00,000

= Rs 4,00,000

\(\therefore\) VAT amount = Rs 4,00,000

Solution:

Given information,

Original Income = Rs 70

New Price = Rs 80

Percentage increase = \(\frac{Amount of change}{Original value}\) × 100

= \(\frac{10}{70}\)× 100

= \(\frac{1000}{70}\)

= 14\(\frac{2}{7}\) %

∴The Price is increased by 14 \(\frac{2}{7}\) %

Solution:

Given information,

Since Nargis spends 65% of his salary, He saves (100 - 65%) = 35% of his salary.

Given, 35% of his salary = Rs 525

\(\frac{35}{100}\) × his salary = Rs 525

∴ His Salary = Rs 525× \(\frac{100}{35}\)

= Rs 1500

Solution:

Here, Rs 10% of Rs 250

\(\frac{10}{100}\)\(\times\) 250

= Rs 25

Solution:

Let x of 25% = 12.5 days.

Or, x \(\times\)\(\frac{25}{100}\) = 12.5

Or, x = \(\frac{12.5\times100}{25}\)

= 50

Hence, 25% of 12.5 days = 50 days.

Solution:

Given information:

Price of the shirt = Rs 500

Price after discount = Rs 420

Actual discount = Rs 500 - Rs 420 = Rs 80

Hence, discount percentage =\(\frac{discount amount}{Total amount }\) \(\times\)100%

= \(\frac{80}{500}\) \(\times\) 100%

= 16%

0%
  • Sita gets 65 marks out of 80. What percent marks did she get?

    60.62 %
    75.85 %
    81.25 %
    80 %
  • Puja deposits $ 1800 per month in her savings bank account. If this is 20 % of the monthly income, find her monthly income.

    $8500
    $9000
    $7000
    $1000
  • Salina scored 90 % marks in maths, 85 % in science, 80 % marks in social sciences and 75 % in languages. If the maximum mark in maths is 200, in science 150, in social sciences 150 and languages 100, find her aggregate percentage.

    80.75 %
    83.75 %
    93.77 %
    63.25 %
  • Find 40 % of 240

    96
    90
    102
    88
  • Find 10 % of 1 hour

    10 minutes
    6 minutes
    5 minutes
    2 minutes
  • Find 120 % of 25 km

    ;i:4;s:5:
    ;i:1;s:11:
    ;i:2;s:5:
    ;i:3;s:5:
  • Find 10 % of 400 kg

    25 kg 
    40 kg
    20 kg
    30 kg 
  • Find the number whose 8 % is 72.

    900
    300
    200
    550
  • In a public show 75 % of the seats were filled. If there were 600 seats in the hall, how many seats were vacant?

    120
    130
    166
    150.
  • Find (frac{25}{8}) % of 160.

    7
    8
    6
    5
  • A team lost 25 % of the matches it played. If it won 15 matches, find the number of matches it played.

    15
    10
    36
    20
  • A number is reduced by 90 %. Its present value is 270. What was its original value?

    150
    300
    200
    350
  • Aakriti spends 65% of his salary and saves Rs 525 per months.Find her salary per month.

    1200
    1500
    2000
    1800
  • The population in a small village increases from 20000 to 21250 in one year. Find the percentage increase in population.

    6.25%
    5 %
    7.36 %
    5.25%
  • Sila scored 36 marks out of 60. Express the marks in percentage.

    65 %
    50 %
    64.25 %
    60 %
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