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 . 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.
3) How to convert a percent into a fraction: Divide the number by 100 and drop the percent symbol, e.g. 60%
4) The percentage of a given number 'n' is given by;
x % of a given number 'n' =
E.g. 70% of 200 =* 200 = 140
Some quicker methods:
1) If two values are respectively x% and y% more than a third value, the first value is % of the second value.
And, the second value is% of the first value.
2) If two values are respectively x% and y% less than a third value, the first value is% of the second value.
And, the second value is % 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;
If the price of a commodity decreases by x %, the increase in consumption so as not to decrease the expenditure is given by;
4) If A is x% of C and B is y% of C, A would be* 100 % of B.
5) Percentage fraction table: Some important fractions to remember
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 wasin 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;
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;
And, if the population decreases by y % in the second year, the population after three years is given by;
Similarly, if the present population of a city changes (increases or decreases) at r % per annum, the population after n years is given by;
And, the population n years ago is given by;
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 % less than the first number, e.g. If A's income is r % more than B's income, B's income is % less than A's income.
9) If a number is r % less than the second number, the second number will be % 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 .
11) If a value is first increased by x %, decreased by y%, there will be % 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;
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 =
'+' 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;
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;
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;
'+' 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
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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