We all use percentage in our daily routine. The term percent mans for every hundred. In its simplest sense percent i.e. per hundred. Thus the expression 20% means 20/100
To express n% as a fraction: n%/100
To express a/b as percentage: (a/b x 100)%
Thus 3/5= (3/5 x100)%
For example: India won 50% of the matches she played means India played 100 matches and won 50 out of them. Pay close attention to “50% of the matches she played” Suppose India played 30 matches then number of matches won by India= 50% of 30
i.e. 30 x 50 /100=15
As seen above n% is nothing but a fraction with numerator n and denominator 100. By remembering certain percentage in reduced form of fraction can be very useful during exams.
½=50% 1/3=33.33%, ¼=25%
1/5=20% 1/6=16.66% 1/8=12.5%
1/9=11.11% 1/11=9.09% 1/12=8.33%
1/15=6.66% 1/16=6.25% 1/20=5%
2/3=66.66% ¾=75% 5/6=83.33%
3/8=37.5% 5/8=62.5% 7/8=87.5%
We will see in further chapter of Ratio that ratio is nothing but fraction. Thus there is strong relation between fraction, ratio and percentage.
For example : In a mixture of 40 liter of milk and 30 liter of water , the ratio of milk an water is 2:3. So this can be converted to fraction of milk as 2/5th. As seen 2/5 = 2/5X100=40%
Concept of Multiplying Factor:
Consider the following calculation when 60 has to be increased by 20%.
Increased value= 60 + 20% of 60
=60+ 20×60/100= 72
One can be rearrange this in following manner
=60 x 1.2=> 72
Here 1.2 can be called multiplying factor. It can be simplifying lots of calculation.
Tips and Tricks with Example:
Shortcut tricks 1: If two values are respectively a% and b% more than third value then the first is (100+a/100+b)/100 % of the second.
For example: If two numbers are respectively 30% and 50 % more than a third then first is the
(100+30/100+50)x 100= (130/150 )x 100= 86.66% of the second.
If A is p% of C and B is q% of C, then A is p/q x 100 % of B.
For Example: If two numbers are respectively 30% and 40% of a third number. Then first of second in percentage = 30/40 X 100= 75%
If price of commodity is increased by r% , then the reduction in consumption so as not to increase the expenditure , is
[r/(100+r) x100] %
If price of commodity is decreased by r% , then the increase in consumption so as not to decrease the expenditure , is
[r/(100-r) x100] %
If the original population of town is P, and the annual increase is r% the population after n year =
P (1+r/100) n
For Example: If annual increase in population of town is 4% and present number of people is 15,625, then population after 3 year
If the original population of town is P, and the annual decrease is r% the population after n year =
P (1-r/100) n
For Example: If annual decrease in population of town is 4% and population two year ago was is 62,500, then present population
If first value is r% more than second value, then the second is [r/(100+r) x 100] % less than the first value.
For Example Ram’s salary is 30% more than that Of Rahul, then Rahul salary is (30/130 x 100 )= 23.07% less than Ram.
If first value is r% less than second value, then the second is [r/(100-r) x 100] % more than the first value.
For Example Ram’s salary is 30% less than that Of Rahul, then Rahul salary is (30/70 x 100 )= 42.85% more than Ram.
Successive Percentage Change
If the value is increased and decreased successively by a% and b% then final increase is given by
The value is increased or decreased according to positive and negative sign obtained.
If the price of petrol increased successively by 20% and then by 10% the net change in percentage term=
The same concept is apply to any relation of this type. Few relations of this types are
Area= Length x Breath
Total sales in rupees= Sales in volumes x Rupees per units
Total sales= Market shares x Total market sales
If the order of increased and decreased is changed, the result remain unaffected so in general
Effect= % increase-% decrease- (% increase x %decrease)/100
The value is increased or decreased according to +ve or –Ve sign obtained.
If the value is first increased by a% and then decreased by a% then net change is a2/100
The salary of worker is first increased by 10% and then decreased by 10 % then change in their salary is 102/100=1%