The study of percentages and applying the percentage formula is necessary. Many works get done by it. The knowledge of what is a percentage, what does it mean, where we can apply the formula, and what help it does, is crucial to mathematics and daily usage. It is also very important and basic quantitative maths. Problems with percentages are very common in competitive exams as well as school tests. Percentage means to find what a number means out of a hundred.

Meaning of percentages –

The term percentage comes from breaking it – “per” “cent”. It means to find what a value does a number or figure has out of a hundred. It means the figure in question is split into 100 equal parts, each meaning a percent.

Calculating percentage formulas makes our life and big sums easier. Because working with so big a digit is a hundred times tougher than working with each separately. The percentage seems to help us in that way. The comparison between percentages is also easy given the fact that the denominator will always be 100.

Some Formulas for the percentage

1. To convert a fraction into a percentage, multiply by 100. Eg: (5/10)*100 = 50%
2. To convert a percentage into a fraction, divide by 100. Eg: 50% = 50/100 = 5/10.
3. x% of y = (x/100)*y
4. In an exam, if the passing percentage is determined to be a minimum of a% and a student scores b marks, however, he manages to fail as he gets only c marks, then the total number of marks the examination holds can be determined by using this formula – 100 x (b + c)/a.
5. Convert ‘x’ SGPA to percentage = (x*10)-7.5
6. The increase in Percentage will be = [(Increase in Value – The Original Value)/The Original Value] x 100
7. The Decrease in Percentage will be = [(The Original Value – The Decrease in Value)/The Original Value] x 100
8. If a fixed number Q is increased by W% and is followed up with another E% and again with R%, then the value of Q will be = [Q(100+W%)(100+E%)(100+R%)].
9. If X is a% of Z and Y is b% of Z, then A = (a/b)*100% of Y
10. If X and Y are multiplied to have a result, and then X is changed by a% and Y is changed by b% then the net percentage change will be [a+b+(ab/100)]%

Few Examples

1) Find out 40% of Rs 200.

1. 50
2. 100
3. 80
4. 120

Answer: c

Explanation: 

x% of any given number ‘n’ = (x/100)*n.

Here, x = 40 and n = 200.

Therefore, 40% of Rs 200 = (40/100)*200 = Rs 80.

2) A student needs at least 55% marks to pass an exam. If the concerned individual scores 1200 but manage to fail by 780 marks, what would be the total marks of the examination?

1. 3000
2. 3200
3. 4000
4. 3600

Answer: d

Explanation:

Marks secured by the concerned student = 1200

The student fails the exam by 780 marks, hence 

Passing Marks = (Marks obtained + Marks failed to secure) 

= 1200 + 780 = 1980

Considering total marks be Z, then

(55/100) x Z= 1980

Z = 3600

3) If 40% of a certain number is greater than 20% of 6500 by 1900, then find the number.

1. 6000
2. 7000
3. 8000
4. 9000

Answer: c

Explanation:

Let the number be Z.

Then, [(40/100) x Z] – [(20/100)*6500] = 1900

(2/5) x Z = 3200

Z = (3200 x 5)/2 = 8000

Conclusion –

The usage of percentage and application of its formula is far-reaching. It is as important in the subject of mathematics as it is in applying daily common problems. The percentage problems are easy enough only if you pay attention to the tips and tricks. Every formula application and step of solving the problem is crucial.