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Hi friends, thank you so much for the great response to my yesterday's post on

*Partnership problems*. Today I am posting the**introduction and problems on Percentage**. In this post i am covering the basic details of percentage, from our next post we shall cover the problems with Higher difficulty level. Happy Reading :)### Percentage Problems Introduction

50 percent means 50 out of 100.

The symbol

**%**is used to denote percent.
Ex : 20%, 35%, 80% etc.

**Percent to fraction :**To convert percent into fraction, divide the percent by 100.

Ex : 25% = 25/100 = 1/4

**Fraction to percent :**To convert fraction into percent, multiply the fraction by 100.

**Increment Percent = (Increment/Source) x 100**

**Ex**: Increment % in 5 and 3 is (3/5) x 100 = 60%

**Decrement Percent = (Decrement/Source) x 100**

**Ex**: Decrement % in 5 and 8 is (5/8) x 100 = 37.5%

### Some important Percent / Fractions

**100% = 1**

**50% = 1/2**

**25% = 1/4**

**20% = 1/5**

**40% = 2/5**

**60% = 3/5**

**16 2/3% = 1/6**

**33 1/3% = 1/3**

**66 2/3% = 2/3**

**12.5% = 1/8**

**6.25% = 1/16**

**75% = 3/4**

**80% = 4/5**

**10% = 1/10**

**125% = 5/4**

**37 1/2% = 3/8**

**87 1/2% = 7/8**

**Following rules should be kept in mind for solving the questions on percentage**

- For converting a given percentage into a fraction, divide it by 100 or multiply by 1/100.
- For converting a given fraction into a percentage multiply it by 100.
- For converting one given quantity, say,
*x*as a percentage of another given quantity say*y,*find (*x/y*) x 100 **Note**: Percentage is never expressed in any unit like rupees or kilos.- When there are two articles '
*a*' and '*b*' in a group and in the ratio of*a*:*b*then to express any one article as a percentage of the group, divide the article by the total articles of the group and multiply the whole by 100.

###
**Now let's see some basic Examples : **

**Example1 : Express 15% as a fraction**

**Solution :**

15% = 15/100 or 3/20

**Example 2 :**

**Express 1/5 as a percentage**

**Solution :**

**1/5 x 100 = 20 i.e. 20%**

**Example 3 : Find out 20% out of Rs. 650**

**Solution :**

as we know, 20% = 20/100

Example 4 : How many percent is 15 cm of 1 metre ?

Example 4 : How many percent is 15 cm of 1 metre ?

**Solution :**

**Note**: Both quantities are covered into same unit.

**Example 5 : A person spent 85% of his monthly income and thereafter saves Rs. 360 per month. Find out his total income.**

**Solution**:

Suppose his monthly income is Rs. 100

Expenditure = 85% = Rs. 85

Saving = Rs. 100 - 85 = Rs. 15

If saving is Rs. 15 , then income is Rs. 100

If saving is Rs. 360, then the income is = (100 x 360) / 15 = Rs. 2400

**Example 6 : If a student gets 38 marks out of 50, what is the percentage of his obtained marks ?**

**Solution :**

**Percentage of obtained marks = (38/50) x 100 = 76%**

**Example 7 : If two numbers are respectively 30% and 40% more than a third number, what percentage is the first of the second ?**

**Solution :**

Let the third number be 100

First number = 100 + 30% of 100 = 130

and Second number = 100 + 40% of 100 = 140

=> Percentage of the first number to the second number to the second number = (130 x 100) / 140

= 92.85

**Example 8 : A student scores 20% marks and fails by 30 marks while another student who scores 32% marks, gets 42 marks more than the minimum required pass marks. What are the maximum marks for the examination ?**

**Solution :**

**Example 9 : An engineering student has to secure 50% marks to pass. He gets 163 marks and fails by 37 marks. Find the maximum marks.**

**Solution :**

Minimum marks required = 163 + 37 = 200

If 50 are the minimum marks then maximum marks = 100

=> 20 are the minimum marks, then maximum marks = (100 x 200) / 50 = 400

**shared by**

*Aindree Mukherjee*
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