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

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 = Ppercentage formula1 +Rpercentage formula in mathsn
    100
    2. Population n years ago =P
    find percentage1 +Rhow to find percentagen
    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 = Phow to calculate percentage1 -Rpercentage calculatorn
    100
    2. Value of the machine n years ago =P
    percentage formula in excel1 -Rpercent calculatorn
    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.

At last, Thanks for choosing Loud Study.

If you have any doubts or confusion, comment in the comment section below, we will try to resolve it as soon as possible.

No comments

We appreciate your comment! You can either ask a question or review our blog. Thanks!!