8/14/2019 Percent & Percentages
1/3
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
www.MBAtutes.com 1
8/14/2019 Percent & Percentages
2/3
Percent & Percentages
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,
www.MBAtutes.com 2
8/14/2019 Percent & Percentages
3/3
Percent & Percentages
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%.
www.MBAtutes.com 3
Top Related