❝ PERCENTAGE ❞

☀ Percentage: Percentage refers to " Per thousand " i,e 8% means 8 out of hundred
or 8/100. A percentage is denoted by %.
a represented as the percent of b as, a/b ×100
b% of a = a × b/100
To Convert a fraction / Decimal into a percentage multiply it by 100.
As 0.35 = 35/100 = (35 ×100)/100%
Rule 1. if x is reduced to x°, then,
Reduce % = {(x - x°/x)}/100
Rule 2. if x increased to x1, then , Increment % = (x1-x/x) ×100
Rule 3. if an amount is increased by a% and then it is reduced by a% again, then,
percentage change will be a decrease of a2/100%
Rule 4. if a number is increased by a% and then it is decreased by b%, then
resultant change in percentage will {a-b-(ab)/100}%
[Negative for decrease, positive for increase]
Rule 5. if a number is decreased by a% and then it is increased by b% then, net
increase or decrease percent is
{-a + b - ( ab )/ 100 } %
[Negative for decrease, Positive sign for increase]
Rule 6. if a number is first decreased by a% and then by b% then net decrease
percent is {-a-b+(ab)/100}%
Rule 7. if a number is first increased by a% and then again increased by b% then
the total increase percent is {a+b+(ab)/100}.
Rule 8. if the cost of an article s increased by A% then how much to decrease the
consumption of the article, so that expenditure remains the same is given by
OR
if the income of a man is A% more than another man then the income of another man
is less in comparison
to the 1st man by {A/(100+A)×100}%
Rule 9. If the cost of an article is decreased by A% then the increase in
consumption of article to maintain the expenditure will be?
OR
if 'x' is A% less than 'y' then y is more than 'x' by Required % = {A/(100-A)×100}%
( increase)
Rule 10. if the length of a rectangle is increased by a% and breadth is increased
by b%, then the area of the rectangle will increase by
Required Increase = { a+b+(ab)/100}%
Rule 11. if the side of a square is increased by a% then its area will be increased
by (2a+a2/100)%
Rule 12. if the side of a square is decreased by a% then the area of the square
will decrease by
∴ Decrease = ( -2a+a2/100)%
Rule 13. if the length breadth and height of a cuboid are increase by a% b% and c%
respectively ,then Increase % in volume [ a + b + c + (ab + bc + ca) / 100 +
( abc )/ (100)2]%
Rule 14. if every side of the cube is increased by a% then increase % in volume
={3a + 3a2/ 100 + a3/( 100 )2 }%
Rule 15. if a% of a certain sum is taken by 1st man and b% of a remaining sum is
taken by 2nd man and finally, c% of a remaining sum is taken by 3rd man, then if
‘x’ rupee is the remaining amount then Initial amount = {100 × 100 × 100 × x
}/( 100 - a )( 100 - b )( 100 - c)
Rule 16. if an amount is increased by a% and then again increase by b% and finally
increase by c%, So, that resultant amount is 'x' rupees. then,
Initial amount = {100 × 100 ×100 × x }/ (100+a)(100+b)(100+c)
Rule 17. If the population/cost of a certain town/ article, is P and the annual
increment rate is r%, then
(i) After 't' years population / cost = P(1+r/100)t
(ii) Before 't' years population /cost = P / (1+r/100)t
Rule 18. if the population /cost of a town /article is P and it decrease / reduces
at the rate o r% annually , then (i) After 't' years population /cost =
P(1-r/100)t
(ii) Before 't' years population / cost = P/(1-r/100)t
Rule 19. On increasing/decreasing the cost of a certain article by x%, a person can
buy ‘a’ kg article less/more in ‘y’ rupees, then
Increased/decreased cost of the article = ( xy/100 ×a)
And initial cost = xy/(100 ± x ) a
[Negative sign when decreasing and positive sign when increasing]
Rule20. if a person saves 'R' rupees after spending x% on food, y% on cloth and z%
on the entertainment of his income then, Monthly income
= 100R/ 100 - ( x + y + z)
Rule 21. The amount of acid /milk is x% in the 'M' liter mixture. How much water
should be mixed in it? so that percentage amount of acid/water would be y% Amount
of water = M ( x - y )/ y
Rule 22. An examine scored m% marks in the exam and failed by p marks. In the same
examination, another examinee obtained n% marks and passed with q more marks than
the minimum then
∴ Maximum marks = 100 ×( p + q )/( n - m)
Rule 23. In the examination, a% candidates failed in Math and b% candidates failed
in English. if c% candidates failed in both the subjects, then
(i) Passed candidates in both the subjects = 100 - (a + b - c)%
(ii) Percentage of candidates who failed in either subject = ( a + b - c)%
Rule 24. In a certain examination, 'B' boys and 'G' girls participated. b% of boys
and g% of girls passed the examination then,
Percentage of passed students of the total students = {( B.b + G.g )/( B + G )}%
Rule 25. In a certain examination, the passing mark is a%. if any candidate
obtains 'b' marks and fails by 'c' marks then,
Total marks = 100(b+c)/a
Rule 26. If a candidate got A% votes in a poll and he won or defeated by 'x' votes,
then, what was the total no. of votes which was cast in a poll?
∴ Total no of votes = (50 ×x) /(50-A)
Rule 27. If a number 'a' is increased or decrease by b%, then the new number will
be
{(100±b)/100} ×a
Rule 28. If two numbers are respectively x% and y% less than the third number, the
first number as a percentage of second is {( 100 - x )/ ( 100 - x) } × 100%
Rule 29. if two numbers are respectively x% and y% more than a third number the
first as a percentage of second is {( 100 + x )/( 100 + y) } × 100%
Rule 30. If the price of an article is reduced by a% and buyer gets c kg more for
some Rs. b the new price per kg of article = ab / (100 × c)
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