Percent & Percentages

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Percent & Percentages

PERCENT AND PERCENTAGES

Definition : Percentage is a fraction, whose denominator is 100. The term per cent means for every

100.The numerator of the fraction is called the rate per cent. Percentage is usually denoted by the sign% and sometimes shortened as p.c.

Percentage explains the increase, the decrease , profit, loss, commission, brokerage etc. With theunit as 100.

To get the per cent profit, the formula to be used is as follows :

Per cent profit =

e.g. : is called 5 per cent( or 5%)

5, which is the numerator is called the rate per cent.

Also, 3% means ( or 3 out of 100).

Percentage is the standard way of comparison of two quantities. If we want to compare two

fractions and , make the denominator 100 for both the fractions.

Therefore, = = 14% ---> means 14 out of 100

Also, = = 32% ---> means 32 out of 100.

Therefore, >

Note the following

1) 5% of Rs. 200 means 5/100 200/1 = 10( of means multiplication)

2) 75% is equivalent to 75/100 =

3) increase % = increase/original 100/1

Before attempting questions on percentage, it is advisable to learn all short forms of percentages.

1) 5% = 5/100 = 1/20 = 0.05

2) 6 % = 25/400 = 1/16 = 0.0625

3) 10 % = 10 / 100 = 1/10 = 0.1

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4) 12 % = 25/100 = 1/8 = 0.125

5) 16 2/3 % = 50/300 = 1/6 = 0.166

6) 20 % = 20/100 = 1/5 = 0.2

7) 25% = 25/100 = = 0.25

8) 33 1/3 % = 100/300 = 1/3 = 0.33

9) 40% = 40/100 = 2/5 =0.4

10) 50% = 50/100 = = 0.5

11) 60% = 60/100 = 3/5 = 0.6

12) 66 2/3 % = 200/300 = 2/3 = 0.66

13) 75% = 75/100 = = 0.75

14) 80% = 80/100 = 4/5 = 0.8

15) 90% = 90/100 = 9/10 = 0.9

16) 100% = 100/100 = 1

17) 125% = 125/100 = 5/4 = 1.25

18) 150% = 150/100 = 3/2 = 1.5

Illustrative Examples

1. Usha deposits Rs. 500 in postal savings account. If this is 20% of her monthly income, what is hermonthly income ( in rs)?

Solution :-

Given,

20% of his monthly income = Rs. 500

20% = 1/5th of monthly income.

Monthly income = Rs. 500 5 = Rs. 2,500.

2. In a container of fruits, there are 25% apples, 40% chikoos and the rest are pineapples. If there are2000 fruits in the container, how many pineapples are there in the container ?

Solution :-

Given,

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Total numbers of fruits in the container = 2000

Apples are 25% of them = of 2000 = 500

Chikoos are 40% of them = 2/5 2000 = 800

Pineapples are ( 2000 500 800) = 700

3. In an examination, a candidate who scores 25% of the maximum marks, fails by 60 marks. Anothercandidate who secures 42% of the maximum marks gets 8 marks more than necessary for passing.Find the maximum marks and the percentage necessary for passing.

Solution :-

Let us assume that the maximum marks are m

Marks scored by the first candidate = 25% of m = m/4

But this candidate failed by 60 marks.

Therefore, marks required for passing = (m/4 + 60).................(1)

Marks scored by the second candidate = 42% of m. This candidate has got 8 marks more thannecessary for passing. Therefore , minimum marks for passing ( 42m/100 8)......(2)

Since the passing marks are same for both candidates, we can equate (1) and (2)

(m/4 + 60) = (42m/100 8)

42m/100 m/4 = 60 + 8

42m 25m / 100 = 68

17m = 6800 m = 6800/17 = 400

Minimum marks for passing = (25% of 400 + 60) = 100 + 60 = 160

% necessary for passing = (160/400) 100 = 40%.

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