Sunday 21 February 2016

Percentages

Percentages
Hello Friends!
Welcome to DIKSHA EDUTECH

In this post, we are going to discuss percentages questions.

‘ Percentage  topic’ is conceptually  very easy to understand. But real fight is in its application. Questions directly on percentage are only asked in ‘ simplification  topic ‘Banking exams or SSC exams. However, percentages is widely used in many other topic including Data Interpretation. If we master the art of ‘ application of percentages’ then it is easy to score good marks.
Meaning: It is a fraction where denominator is 100 and Numerator is called Rate percent.
‘‘Percent’ comes from the Latin phrase per centum, which means per hundred
Thus, Percentage =  for every hundred.

example:
30% = 30/100 =  3/10
⅜  =  (3/8)*100 =  37.5%

Formula1:
X % of Y =  Y % of X   =  XY/100

  1. 50% of ?   = 360
ans:     50 X/100 = 360
            X =   720.

Question:
Ram spends 20% of his monthly salary on house rent, 25% on food, 10% on fuel, 15% on movies and 18% for rent. He saves the remaining amount Rs. 4800. What is his monthly salary?
solution:

Expense =  ( 20% + 25% + 10% + 15% +18% )  =   88%
saving     = (100% - 88% )  =  12%

now, 12% = 4800   ( given in Question)
hence, monthly slary = 100%  =  (4800/12% )*100 %   = (4800* 100%)/ 12%   = 40000.

Formula 2 :
Percentages of percentage
X % of Y % of  Z  =    ( XY/100) % of Z

example: 40% of 50% of 5000    =   (40*50/100)% of 5000    =  20% of 5000   =   1000.

Question:

Shyam decided to donate 30% of her monthly income to a school. But on the day of donation, he decided to donate only 4200, which is 70% of what he had earlier decided. What should be the actual donation as per earlier decision?
solution:

70% of  30%  =   4200    = (70*30)% of 4200 = 21% = 4200
[ using X % of Y % of  Z  =    ( XY/100) % of Z]
actual donation , 30%         = ?
=   (30*4200/21) = 6000
actual donation = 6000


Question:

In an election between 2 candidates, 10% votes cast are  invalid. The winner get 70% of the valid votes and defeats the loser by 1800 votes. How many votes were totally cast?

winner gets 70% of 90% of total votes  [ since, 10% votes were invalid]
loser  gets    30% of 90% of total votes

Margin of win  =   63% - 27%  =  1800 ( given in question)
                            36%  =  1800
              hence,   100%  =?   =   (1800*/36)100   =  5000.  



Formula 3:
X is what  % of Y  =    (X/Y)*100

question: In an exam, Ram scored 30% less than  shyam and Manish scored 20% less than shyam . Ram ‘s score is what % of Manish’s score?

solution:
here, comparision of Ram and Manish Is w.r.t. Shyam,
Hence, Let,  Shyam =  100%.
           then, Ram    =  70% and Manish  =  80%

now, ( Ram/ Manish)*100  = (70%/ 80%) * 100  =     700/8 = 87.5.

Formula 4:

 X is what % more ( or less) than Y  =  (X-Y)*100/ Y

                                                  here  (-) ve sign indicates = less = ( X
                                                   (+) ve sign indicates= More = ( X> Y)        

example:
Ram salary is 25% more than Shyam’s salary. Then by what percent is   Shyam’s  salary less than Ram’s?   

Let,  Shyam’s salary = 100 %, then Ram’s salary = 125%

shyam’ salary is = (100% -125%)*100/125     =  (-) 20%.         

Formula 5:                                                                                                                                     

Percentage change =  [ final value -  Initial Value]*100/ initial value

Formula 6:

effective percentage change  =  [ X + Y +  ( XY/100)   ] %

here, X and Y are percentage change in 2 variables.

example:

The length of a rectangle is increased by 40% and its breadth increased by 20%. What will be the percentage change in the  area of rectangle?

Solution: Effective percentage change   =  [ 40 + 20 +( 40*20/100)] %   =   68%


Visit Us:      www.dikshaedutech.com