Mathematics: Tips for Solving Percentage Problems in Competitive Exams

Tips for Solving Percentage Problems

In mathematics, percentage is a way of expressing a number as a fraction of 100 (per cent means per hundred). It is often denoted using the percent sign, "%" Ex:- 45% (read as "forty fiver percent") is equal to 45/100 or 0.45.

The percentage is used to express how large quantity and small quantity are related to another quantity. It has using two quantities; usually the first quantity represents the part of second quantity and it should be greater than zero. Percentage helps to find and express numbers between zero and one, any dimensionless proportionality can be expressed as a percentage.

Ex:- 129% is 1.29 and 0.29% is 0.0029.

How to Solve the Percentage Problems:

• For converting a fraction and a decimal to a percentage, multiply it by hundred.
• For converting a percentage to a fraction and decimal, divide by hundred.
• We can write a fraction and a decimal as a percentage.

Example 1:-  What is the Percentage of 79% ?

Solution:- 79/100 = 0.79

Example 2:-  Define 2 ½ % as a fraction.

                                  2½         5 /2          5          1

 Solution:-  2½  % =  ------  =   ----   =  ----   =  ----

                                  100          100        200       40  

Example 3: -

A basket contains 250 eggs. 150 were not broken. What percentage of the eggs were broken ?

Solution:- Number of eggs = 250

               

            Number of eggs not broken = 150

There fore Number of eggs broken = 250- 150 = 100

                                           100

Broken egg's percentage = -----  x 100% = 40 %

                                          150

Example 4:- What is the value of 84.5% of 46 ?

                             84.5   

Solution:- 84.5 = ------- x 46  = 0.845 x 46  = 38.87

                             100

Example 5:- What  percentage of 2.75 is 25 ?

                                                         25   

Solution:- Required percentage = -------- x 100

                                                        2.75

                                              

                                             =  9.09%