DEFINITION:-

A fraction whose denominator is 100 is called a percentage & the denominator of the fraction is called the rate of percent (%).

Percent as a Fraction:-

1)35% = 35/100 = 7/20
2)12% = 12/100 = 3/25

Percent in decimal form:-

1)65% = 65/100 = 0.65
2)73% = 73/100 = 0.73

Some important Rules:

1.If ‘A’ is R% more than B, then;

  ‘B’ is less than A by : 

2.If ‘A’ is R% Less than B, then;

'B' is more than A by ;

3.The Price of a commodity increases by R% then reduce in consumption not to increase the expenditure is

4.If the price of a commodity decreases by R% then the increase in consumption not be decrease the expenditure is

Rules on Population:-

Let the present population of a town be ‘P’ now and suppose it increases at the rate of R% p.a., then,

i)Population after ‘n’ years =

ii)Population  ‘n’ years ago =

Results on decreciation:-

Let the present value of a machine be ‘P’ now and suppose it depreciates at the rate of R% p.a. then

i)Value of the machine after ‘n’ years =

ii)Value of the machine ‘n’ years ago =

Results on increases & decreases of the two values:-

1.If the value is increased successively x% and y% then the final increase is given by :

2. If the value of a number is first increased by x% and later decreased by y%, then there is %increase / decrease according to the sign value

3.If the value of a number is first increased by x% and later decreased by x%, then the net change is always decrease, which is equal to

4.If the value is decreased successively x% & y% then final decrease is given by :

Important Theorem :-

If the sides of a triangle, rectangle, square, circle, rhombus (or any two – dimensional figure) are

i)increased by x%, its area is increased by :

ii)decreased by x%, its area is decreased by :

Practice following examples

1)What % of 40 minutes is 24 seconds?

2)455 ÷ 13 + ?% of 680 = 205

3)0.07% of 1180 - 0.03% of 380 = ?

4)34% of 320 + ?% of 460 = 237.6

5)7.4% of 3455 + 6.25% of 2.9328 = ?

6)A's income is 25% more than B's income. The % of B's income in terms of A's income is ?

Answers:

1)40x60 / 100 ( or 2400 seconds/100)=24 Seconds

2) 25; =>?% of 680 = 205 - 35; =>?=170 x 100/680 = 25 ;

3) =>0.07/100 * 1180 - 0.03/100 x 380; =>0.826-0.114=0.712;

4) =>108.8 + ? x 4.6 = 237.6; ?=237.6-108.8/4.6 = 28;

5) 274;

6) 80%;

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