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**Introduction**

- The chapter on Percentages forms the most important chapter (apart from Number Systems) in the CAT syllabus and the XAT examination. The importance of ‘percentages’ is accentuated by the fact that there are many questions related to the use of percentage in all chapters of commercial arithmetic (especially Profit and Loss, Ratio and Proportion, Time and Work, Time, Speed and Distance).
- Besides, the calculation skills you develop while going through the chapter on percentages will help you handle
**Data Interpretation (DI) calculations**. A closer look at that topic will yield that**at least 80% of the total calculations**in any DI paper constitute calculations on additions and percentage.

__Have a look at CAT 2019's question that is a mix of Percentages and Profit & Loss chapters:__

- CAT likes to
**mix the concepts**in the questions. You can expect the same in**CAT 2021**as well. That is the reason why you need good practice on questions to ace the**Quant & DI section.** **So how do you do that?**- Don't worry, we have covered that for you at EduRev.

**Definition**

- ‘Percent’ as the name suggests ‘per’ means
**every**and ‘cent’ means**hundred**i.e. “for every hundred”. - It is an important tool for the comparison of data and information.

**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%.

**Concept of Percentage**

- A percentage can only be calculated if it has a base value or denominator.
- In the above example, the base value or denominator was 40, which means to say that Ana secured 20 marks out of 40 (which is the base value of the calculation of marks secured.)
- Concept of percent change = (Final value – initial value)/ initial value * 100

Note:Initial value is taken as base or ‘denominator’ while calculating percent change.

**➢ Percent Point Change**

- It is very important to understand the difference between the percent change and percent point change.
__Let us understand the difference between them by the following example:__► Ana secured 70 percent marks in her last term exam.

► Now, when we say that her marks increased by 5 percent, then this means that there is an increase of 5% marks when compared to the last marks she secured, which is 5% of 70% = 3.5%

► Her new secured marks will be 70 + 3.5 =**73.5%**

► Now, when we say that her marks increased by 5 percentage points, then this means that there is an absolute increase of 5% marks in her marks, irrespective of the last marks she secured, which is her new secured marks will be 70 + 5% =**75%**

Therefore,

Percentage Point Change = Difference of two percentage figures

**Solved Example**

**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

Try yourself:The number of votes not cast for the PNC Party increased by 25% in the National General Election over those not cast for it in the previous Assembly Polls, and the PNC Party lost by a majority twice as large as that by which it had won the Assembly Polls. If a total 2,60,000 people voted each time, how many voted for the PNC Party in the previous Assembly Polls?

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Try yourself:If the price of sugar goes up by 10%, then what should be the percentage decrease in the quantity consumed so that the total expenditure on sugar remains the same?

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Try yourself:Ramu conducts his business in the following manner : Every once in a while he raises his prices by a certain percentage and a while later reduces his price by the same percentage. After one such updown cycle of increasing and then decreasing his price by x%, the price of the commodity decreases by Rs 100. In the next cycle, he increases and decreases his price by (x/2)% and then sells the commodity for Rs 2376. What is the initial price of the commodity?

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Try yourself:**PYQ (CAT 2019): On selling a pen at 5% loss and a book at 15% gain, Karim gains ₹ 7. If he sells the pen at 5% gain and the book at 10% gain, he gains ₹ 13. What is the cost price of the book in Rupees?**

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Try yourself: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?

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