Table of contents  
Introduction  
Definition  
Concept of Percentage  
Solved Examples 
Have a look at CAT 2019's question that is a mix of Percentages and Profit & Loss chapters:
‘Percent’ as the name suggests ‘per’ means every and ‘cent’ means hundred i.e. “for every hundred”.
Example: Ana got 20 marks out of 40. Then, how many marks did she get when compared to 100?
Solution: By unitary method.
In the total of 40 marks, Ana got 20 marks Then,
In the total of 100 marks, Ana would have got = 20/40 *100 = 50 marks
It is just that when expressed in terms of hundred, it becomes percent.
That means to say Ana got 50%.
Note: Initial value is taken as base or ‘denominator’ while calculating percent change.
Percentage Point Change = Difference of two percentage figures
Example 1: A report consists of 20 sheets each of 55 lines and each such line consists of 65 characters. This report is reduced onto sheets each of 65 lines such that each line consists of 70 characters. The percentage reduction in the number of sheets is closest to:
Solution:
No. of Characters in one line = 65
No. of characters in one sheet = No. of lines × No. of characters per line = 55 × 65
Total number of characters = No. of sheets × No. of characters in one sheet = 20 × 55 × 65 = 71500
If the report is retyped:
New sheets have 65 lines, with 70 characters per line
No. of characters in one sheet = 65 × 70
Number of pages required:
Hence, 16 pages will be required if the report is retyped.
Hence, reduction of (20 – 16) = 4 pages
% reduction is = (4/20) × 100 = 20%
Example 2: 2/5th of the voters promise to vote for A and the rest promised to vote for B. Of these, on the last day, 15% of the voters went back of their promise to vote for A and 25% of voters went back of their promise to vote for B, and A lost by 200 votes. Then, the total number of voters is:
Solution:
Let x be the total number of voters.
Voters promised to A = 2/5 x
Voters backed out = 15% of 2/5 x
Voters promised to B = 3/5 x
Voters backed out = 25% of 3/5 x
Total Number of votes for A = (2/5x) – (15% of 2/5x) + (25% of 3/5x)
Total Number of votes for B = (3/5x) – (25% 0f 3/5x) + (15% of 2/5x)
Give Difference in votes is 200
Therefore,
So, there were 10000 voters.
Example 3. A person who has a certain amount with him goes to market. He can buy 50 oranges or 40 mangoes. He retains 10% of the amount for taxi fares and buys 20 mangoes and of the balance, he purchases oranges. The number of oranges he can purchase is:
Solution:
The person can buy 50 oranges or 40 mangoes.
Let the price of one orange be Rs. x
The total amount the person has = Rs. 50x
40 mangoes cost 50x, So one mango costs 1.25x
10% of the total amount is retained for taxi fare = 10% of 50x = 5x
20 mangoes bought for 20 * 1.25x = 25x
Money left with the person = 50x – (Taxi fare) – (Mangoes cost) = 50x – 5x – 25x = 20x
One Orange was for Rs. x, Therefore, 20 oranges can be bought with Rs. 20 x
Thus, the person bought 20 oranges.
Example 4. Forty percent of the employees of a certain company are men and 75% of the men earn more than Rs. 25,000 per year. If 45% of the company’s employees earn more than Rs. 25,000 per year, what fraction of the women employed by the company earned Rs. 25,000 or less per year?
Solution:
Let the total number of employees in the company be x
Then the number of men and women be 0.4x and 0.6x, respectively.
75% of men earn more than Rs. 25000 ⇒ 0.75 x 0.4 x = 0.3 x
Total number of employees earning more than Rs. 25000 = 45% x = 0.45 x
Number of women earning more than Rs. 25000 = Total employees earning more than Rs. 25000 – total number of Men earning more than Rs. 25000 = 0.45 x – 0.30 x = 0.15 x
Number of the women earning Rs. 25000 or less = 0.60 x – 0.15 x = 0.45 x
Fraction of the women employed by the company who earn Rs. 25000 or less = (0.45x/0.60x) = 45/60 = 3/4
Example 5: In a class of 60 students, 20% are male. 75% of female students passed an exam conducted for the whole class. What is the number of female students who passed the exam?
Solution: Since it is given that 20% of students are male, that means the remaining 80% are females.
Number of females  (80/100)*60 = 48
Number of female students who passed = 75% of 48 = 36
207 videos156 docs192 tests

1. What is the definition of percentages? 
2. How is the concept of percentage used in everyday life? 
3. How can percentages be calculated? 
4. Can percentages be added or subtracted? 
5. How can percentages be used to solve reallife problems? 
207 videos156 docs192 tests


Explore Courses for UPSC exam
