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Percentage Concepts and Formulas

Points to remember:

1) The term percent comes from the Latin phrase 'per centum' which means per hundred or for every hundred. It is a fraction whose denominator is 100 and numerator is percent, e.g. 40% or Apti Percentage 1. In mathematics, percent is denoted by the symbol '%'.

2) How to convert a fraction into a percent: To convert a fraction into percent multiply it by 100, e.g. Apti Percentage 2

3) How to convert a percent into a fraction: Divide the number by 100 and drop the percent symbol, e.g. 60% Apti Percentage 3

4) The percentage of a given number 'n' is given by;

x % of a given number 'n' =Apti Percentage 4

E.g. 70% of 200 =Apti Percentage 5* 200 = 140


Some quicker methods:

1) If two values are respectively x% and y% more than a third value, the first value is Apti Percentage 6% of the second value.

And, the second value isApti Percentage 7% of the first value.

2) If two values are respectively x% and y% less than a third value, the first value isApti Percentage 8% of the second value.

And, the second value is Apti Percentage 9% of the first value.

3) If the price of a commodity increases by x %, the reduction in consumption so as not to increase the expenditure is given by;

Apti Percentage 10

If the price of a commodity decreases by x %, the increase in consumption so as not to decrease the expenditure is given by;

Apti Percentage 11

4) If A is x% of C and B is y% of C, A would beApti Percentage 12* 100 % of B.

5) Percentage fraction table: Some important fractions to remember

Apti Percentage 11

5) x % of a quantity is taken by A, y % of the remaining is taken by B and z % of the remaining is taken by C. If P is left in the fund, there wasApti Percentage 13in the beginning.

6) x % of a quantity is added, y% of the increased quantity is added, again z % of the increased quantity is added and it becomes A, the initial amount is given by;

Apti Percentage 14

7) The population of a town is P. If it increases by x % in the first year, y % in the second year and z% in the third year, the final population after three years is given by;

Apti Percentage 15

And, if the population decreases by y % in the second year, the population after three years is given by;

Apti Percentage 16

Similarly, if the present population of a city changes (increases or decreases) at r % per annum, the population after n years is given by;

Apti Percentage 17

And, the population n years ago is given by;

Apti Percentage 18

Note: Use '+' sigh if the population is increasing at r % per annum and use '-' sign if it is decreasing at r % per annum.

8) If a number is r % more than the second number, the second number will be Apti Percentage 19% less than the first number, e.g. If A's income is r % more than B's income, B's income is Apti Percentage 20% less than A's income.

9) If a number is r % less than the second number, the second number will be Apti Percentage 21% more than the first number.

10) If a value is increased by x % and later decreased by x %, net change in the value is always a decrease which is equal to x % of x or Apti Percentage 22.

11) If a value is first increased by x %, decreased by y%, there will be Apti Percentage 23% increase or decrease in the value, i.e. '+' sign will show an increase and '- 'sign will show a decrease in the value.

12) If a value is increased by x % and y % successively, the final increase in the value is given by;

Apti Percentage 24

13) If the price of a product is reduced by x % and its consumption is increased by y % or the price is increased by x % and consumption is decreased by y%, the effect on revenue is given by;

= percent increase - percent decrease =Apti Percentage 25

'+' sign will show an increase and '-' sign will show a decrease in the value.

14) The pass marks in an examination are x %. If a student secures y marks and fails by z marks, the maximum marks are given by;

Apti Percentage 26

15) A candidate scores x % marks in an examination and fails by 'a' marks. If another candidate who scores y % marks which is 'b' marks more than the required pass marks, the maximum marks for this examination are given by;

Apti Percentage 27

16) The sides of a triangle are measured. If one side is taken x % in excess and the other side is taken y% in deficit, the error percent in area calculated from these measurements is given by;

Apti Percentage 28

'+' sign will show the excess and '-' sign will show the deficit in the area.

17) If the sides of a triangle, rectangle, square or any other two-dimensional shape are increased by x %, the area is increased by Apti Percentage 29

18) In an examination, x% students failed in one subject and y% students failed in another subject. If z% students failed in both the subjects, the percentage of students who passed in both the subjects is given by;

= 100 - (x + y - z)



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