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**Percentages**

‘Percent’ as the name suggests ‘per’ means **every **and ‘cent’ means- **hundred** i.e. “for every hundred”.

It is an important tool for comparison of data and information.

**Percentage**

**Example****: ****Ana got 20 marks out of 40. Then, how much marks did she get when compared to 100?****Solution **- By unitary method. In total of 40 marks Ana got 20 marks, Then, In total of 100 marks Ana would have got = 20/40 *100 (Unitary method)

= 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 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 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 then by a 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 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 **

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 report is retyped.

Hence, reduction of (20 – 16) = 4 pages

% reduction is = (4/20) × 100 = 20%

Question 2: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?

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 = 2/5 x – 15% of 2/5 x + 25% of 3/5 x

Total Number of votes for B = 3/5 x – 25% 0f 3/5 x + 15% of 2/5x

Give Difference in votes is 200

Therefore,

So, there were 10000 voters.

The person can buy 50 oranges or 40 mangoes.

Let the price of one orange be Rs. x

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 x 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.

Question 3: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?

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 = ¾

Question 4: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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### Test: Percentages- 4

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### Test: Percentages- 5

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- Test: Percentages- 3
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- Test: Percentages- 2
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