BCS Mathematics | part-3 | bcs preparation | preliminary preparation | competitive exam preparation

Описание: BCS Mathematics | part-3 | bcs preparation | preliminary preparation | competitive exam preparation

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In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It represented by the symbol “%”.

Examples of percentages are:

10% is equal to 1/10 fraction
20% is equivalent to ⅕ fraction
25% is equivalent to ¼ fraction
50% is equivalent to ½ fraction
75% is equivalent to ¾ fraction
90% is equivalent to 9/10 fraction
Percentages have no dimension. Hence it is called a dimensionless number. If we say, 50% of a number, then it means 50 per cent of its whole.

Percentages can also be represented in decimal or fraction form, such as 0.6%, 0.25%, etc. In academics, the marks obtained in any subject are calculated in terms of percentage. Like, Ram has got 78% of marks in his final exam. So, this percentage is calculated on account of total marks obtained by Ram, in all subjects to the total marks.
Percentage Formula
To determine the percentage, we have to divide the value by the total value and then multiply the resultant to 100.

Percentage formula = (Value/Total value)×100

Example: 2/5 × 100 = 0.4 × 100 = 40 per cent

How to calculate the percentage of a number?
To calculate the percentage of a number, we need to use a different formula such as:

P% of Number = X

where X is the required percentage.

If we remove the % sign, then we need to express the above formulas as;

P/100 * Number = X

Example: Calculate 10% of 80.

Let 10% of 80 = X

10/100 * 80 = X

X = 8

Percentage Difference Formula
If we are given with two values and we need to find the percentage difference between the two values, then it can be done using the formula:

Percentage Difference=|N1−N2|[(N1+N2)2]×100

For example, if 20 and 30 are two different values, then the percentage difference between them will be:

% difference between 20 and 30 = Percentage Difference=|20−30|[(20+30)2]×100

Percentage Increase and Decrease
The percentage increase is equal to the subtraction of original number from a new number, divided by the original number and multiplied by 100.

% increase = [(New number – Original number)/Original number] x 100

where,

increase in number = New number – original number

Similarly, percentage decrease is equal to subtraction of new number from original number, divided by original number and multiplied by 100.

% decrease = [(Original number – New number)/Original number] x 100

Where decrease in number = Original number – New number

So basically if the answer is negative then there is percentage decrease.


Solved Example
Two quantities are generally expressed on the basis of their ratios. Here, let us understand the concepts of percentage through a few examples in a much better way.

Examples: Let a bag contain 2 kg of apples and 3kg of grapes. Find the ratio of quantities present, and percentage occupied by each.
Solution: The number of apples and grapes in a bag can be compared in terms of their ratio, i.e. 2:3.

The actual interpretation of percentages can be understood by the following way:

The same quantity can be represented in terms of percentage occupied, which is given as:

Total quantity present = 5 kg

Ratio of apples (in terms of total quantity) = 25

= 25×100100

From the definition of percentage, it is the ratio that is expressed per hundred,

1100=1%

Thus, Percentage of Apples = 25×100=40

Percentage of Grapes = 35×100=60

Fractions Percentage
1/2 50%
1/3 33.33%
1/4 25%
1/5 20%
1/6 16.66%
1/7 14.28%
1/8 12.5%
1/9 11.11%
1/10 10%
1/11 9.09%
1/12 8.33%
1/13 7.69%
1/14 7.14%
1/15 6.66%

Converting Fractions to Percentage
A fraction can be represented by ab.

Multiplying and dividing the fraction by 100, we have

ab×100100

=(ab×100)1100 ………………(i)

From the definition of percentage, we have =1100 = 1%

Thus equation (i) can be written as:

=ab×100%

Thus fraction can be converted to percentage simply by multiplying the given fraction by 100.
Also, read: Ratio To Percentage

Percentage Questions
Q.1: If 16% of 40% of a number is 8, the number is?

Solution: Let the required number be X.

Therefore, as per the given question,

(16/100) x (40/100) x X = 8

So, X = (8 x 100 x 100) / (16 x 40)

= 125

Q.2: What percentage of 2/7 is 1/35 ?

Solution: Suppose X% of 2/7 is 1/35

∴ (2/7 x X) / 100 = 1/35