# Aptitude : Percentage Problems with Explanations - Introduction

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

A fraction with denominator 100 is called percentage. Numerator of that fraction is called rate percent.

The term percent means per every 100.

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.

Ex : 1/5 = (1/5) x 100 = 20%

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
1. For converting a given percentage into a fraction, divide it by 100 or multiply by 1/100.
2. For converting a given fraction into a percentage multiply it by 100.
3. 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.
4. When there are two articles 'a' and 'b' in a group and in the ratio of a : 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 ?

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