PERCENTAGE

INTRODUCTION-
                                 A percentage is a number or ratio expressed as a fraction of 100. The sign for percent is  "%".

Let's take an example.
Ram scores 60 marks in a test whose maximum marks is 100 whereas Shyam scores 70 marks in a test of 140 marks.Who scored better between the two?

Total maximum marks in both the cases are different so we cannot give a verdict about their performances.
That's where percentage comes into the picture.

Ram scored 60 out of 100 i.e; (60*100)/100 %=60%
Shyam scored 70 out of 140 i.e; (70*100)/100 %=50%
Now we can tell who scored better among the two i.e; RAM.

From the above example, we deduce that the one use of percentage is the comparison.

 Let's take an example.
B’s salary is 25% more than A’s salary. By what percent is A’s salary less than B’s salary?

This question can be solved by 3 methods.Choose wisely😛 

 METHOD 1-

Let A's salary be x
B's salary= x+25%x = x+ 25x/100 =1.25x
Difference of their salary= 1.25x-x= 0.25x
Now we have to compare this difference with B's salary,
i.e; 0.25x/1.25x
   =25/125
converting it into percentage we multiply it by 100
=25*100/125 %=20%ANS
METHOD 2-

Instead of X take A's salary as 100. It is very helpful to assume values in such cases to reduce cumbersome calculations.
METHOD 3-

 This method is very useful and you can apply it anywhere.It saves a lot of time and comes handy especially while dealing with Profit/Loss, SI and CI.
A's salary is 25% less than B's.
Converting 25% into a fraction
we get, 25/100 =1/4
Now if A's salary is 4 units B's salary =4+1=5 units
Difference =5-4=1 unit
And we have to compare it B's salary i.e; 5units= 1/5 *100 %=20% ANS

 NOTE- ONE MUST BE QUICK WITH RATIO PERCENTAGE CONVERSION.

Let's solve some of the examples

EXAMPLE 1-  The length and breadth of a rectangle are changed by +20% and by –10%
respectively. What is the percentage change in the area of the rectangle?

 Converting percentage into the ratio, we get
length= 20% = 20/100 = 1/5
Now if the initial length was 5unit,
Length after the increase =5+1=6 units
Similary for breadth = -10% = -10/100 =-1/10
Initial breadth =10 units
New breadth =10-1=9 units

Initial Area= 5*10=50 sq units
New Area = 6*9 = 54 sq uits
Difference =54-50 =4 sq units
% change = (New area - initial area)/Initial area * 100%
                = 4/50 *100 % =8%ANS
Shortcut-
 Let rectangle be of area=10*10
New area= 12*9=108
%age change=8*100/100 %= 8%ANS


EXAMPLE 2-  Due to a 25% price hike in the price of rice, a person is able to purchase 20 kg less of rice for RS.400. Find the initial price.

 General Method-

Price(per kg) * Quantity = 400(constant)
 Original Price = y
final price = 5y/4
As price and quantity are inversly proportional,
Initial quantity = 5/4 final quantity
Let initial quantity be X
X = 5/4(X-20)
X=100kg
Initial price=400/100 =4RS/kgANS

 SHORTCUT-

25% is an increase in the price, converting it into a ratio, we get
25% = 25/100 = 1/4

 If initial price was 4 units,
Final price =4+1=5 units
We know that, price*quantity=constant
now 1 unit difference that results in 20 kg decrease,
So 5units = 20*5 =100kg
Original Price =400/100 = RS.4 ANS

 EXAMPLE 3-In an examination, 48% students failed in Hindi and 32% students in History, 20% students failed in both the subjects. If the number of students who passed the examination was 880, how many students appeared in the examination if the examination consisted only of these two subjects?
TOTAL STUDENTS =100%
Students failed in only Hindi =48% - 20%= 28%
Students failed in only History =32% - 20% =12%
Total students failed=28+12+20 = 60%
%age of students passed= 40%
Now, 40%=880
1%=880/40= 22
100%=22*100 = 2200 ANS









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