PERCENTAGE

What is percentage?
Percentage is a fraction or a numerical expression or a ration with 100 assumed as denominator. So we can represent 1 percentage as 1%.
Points to be remember-

1 = 100%
1/2 = 50%
1/3 = 33%
1/4 = 25%
1/5 = 20%
1/6 = 16%
1/7 = 14%
1/8 = 12%
1/9 = 11%
1/10 = 10%
1/11 = 9%
1/12 = 8%
1/13 = 7%


If the price of a commodity increases by R%,then the reduction in consumption as not to increase the expenditure is =%
 If the price of a commodity decreases by R%, then the increase in consumption as not to decrease the expenditure is= %.

Let the population of a town be P now and suppose it increases at the rate of R% per annul, then:
Population after n years = P (1+R/100)n


Population n years ago =
Let the present value of a machine be P. Suppose it depreciates at the rate of R% per annul, then :
Value of the machine after n years =P (1-R/100)n

Value of the machine n years ago =
If A is R% more than B, then B is less than A by=%
 If A is R% less than B, then B is more than A by= %.


Percentage Type 1 Shortcut Tricks
Example:
If the difference between 45% of a number and 3/5th of that number is 18. What is the number?
Solution:
we know 3/5 = 60%
45% – 60% = 15 %
15% = 18 = 120

Percentage Type2 Shortcut Tricks
Example:
Sahil work in shop and his 30% of income is  Rs.1800 .Find the 65% of his income and also find the 1 / 5 of Sahil’s income.

 1800 x 65 / 30 = 3900.
Shahil's Income = 3900*1/5=780

Example:
Raj spend his money from his saving in different way that is he spends 30% on travel,10% on food,15% on wages and 22% on purchase a bike and after that all expenditure he saved 4600.Find the how much he spent on bike.

The total income as 100% so, (100% – 30%+10%+15%+22%) = 77% and now (100% – 77%) = 23%
 now 4600 x 100/ 23 =20000
Bike Expenditure is 22% so, 20000 x 22 / 100 = 4400.


Example:
Sanjay got 88 marks in Hindi , 81 marks in Science , 74 marks in Maths , 68 marks in Social Science and 57 marks in History . The maximum marks of each subject are 100. How much overall percentage of marks did he get?
Here,88+81+74+68+57=368
5 Subject So=500
Percentage = 368 x 100 / 500 = 73.6