# Percentage : Formula, Shortcut, Tips and Tricks to Solve Problems

Hello Aspirants, In this lesson " Percentage : Formula, Shortcut, Tips and Tricks to Solve Problems " we will cover basic concepts of percentage, formulas, tips, tricks and shortcuts used to solve questions based on percentage.

Now let's start the lesson !

Percent implies " for every hundred " and it is denoted by sign " % " pronounced as percentage.

Accordingly, X % = X / 100, Y % = Y / 100

Now let's see some examples :

2 %  = 2 / 100 = 0.02 ( means 2 parts from 100 )

25 %  = 25 / 100 = 1 / 4 = 0.25 ( means 25 parts out of 100 )

Basic Formula :

To find X % of Y

X % of Y = X / 100 of Y = XY / 100

Now let's see some examples :

25 % of 200 = ( 25 x 200 ) / 100 = 50

50 % of 30 = ( 50 x 30 ) / 100 = 15

Tips : X % of Y = Y % of X i.e. 50 % of 30 = 30 % of 50

To find percent of a number X with respect to Y

Percent of X / Y = ( X / Y ) 100

Now let's see some examples

Percent of ( 2 / 5 ) = ( 2 / 5 ) 100 = 40 %

Percent of ( 20 / 200 ) = ( 20 / 200 ) 100 = 10 %

Some Important Points To Remember :
• If new value of a quantity is n times the previous value, then percentage increase = ( n - 1 ) 100 %
• If the present value X of a quantity is increased by N % then the new value of the quantity = X ( 1 + N / 100 )
• If the present value X of a quantity is decreased by N % then the new value of the quantity = X ( 1 - N / 100 )
• If A is N% more than B, then B is { 100N/( 100 + N )} % less than A.
• If A is N% less than B, then B is { 100N/(100 - N )} % more than A.
• If the value of an item is increased by N%, the percentage reduction that needs to make to bring the original value of item is calculated using formula : { 100N/( 100 + N )} %
• If the value of an item is decreased by N%, the percentage increment that needs to make to bring the original value of item is calculated using formula : { 100N/(100 - N )} %
• If the price of goods increases by N %, then the reduction in consumption so as not to increase the expenditure can be calculated using the formula : { 100N/( 100 + N )} %
• If the price of goods decreases by N %, then the increase in consumption so as not to decrease the expenditure can be calculated using the formula : { 100N/(100 - N )} %
• Let the present population of a town be P. Suppose it increases at the rate of R% per annum. Then:
 1. Population after n years = P 1 + R n 100
2. Population n years ago =P
 1 + R n 100
• Let the present value of a machine be P. Suppose it depreciates at the rate of R% per annum. Then:
 1. Value of the machine after n years = P 1 - R n 100
2. Value of the machine n years ago =P
 1 - R n 100
Successive Percentage : It mainly refers to two or more percentage applied to same item.
Let the current value of an item is N, it goes a percentage change of X % and then Y %,

Then new value of item = N { ( 1 + X / 100 ) ( 1 + Y / 100 ) }

Let the current value of an item is N, it goes a percentage change of X % and then Y % and then Z %,
Then new value of item = N { ( 1 + X / 100 ) ( 1 + Y / 100 ) ( 1 + Z / 100 ) }
Percentage Change : The increase or decrease in percent due to change of successive percentage of an item is called Percentage Change.

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