# Aptitude : Percentage Problems with Explanations - Introduction

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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

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

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
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