Percentages
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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
- 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%
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