Simplifying Quantitative Aptitude: Concepts, Formulae & Tricks for solving Questions in Percentages

Percentage is considered one of the important topics in Quantitative Aptitude section of different exams including Bank, SSC, MBA, CSAT etc. Different types of questions are framed from the topic Percentage. In order to solve questions based on Percentages, one needs to understand the underlying concept, Formulae and tricks involved.

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Percentage Basics:

Per cent means per hundred. For instance 5 % means 5 parts in hundred i.e. 5/100. The concepts of percentage is widely used to solve questions from different topics including, Partnerships, Profit & Loss, Data Interpretation.

Fractional Equivalent of Percentage: For each percentage, there is a corresponding fraction. Sometimes a percentage value that looks odd is having an easier equivalent fraction.

For example 33.33 % is equivalent to 1/3. It means if we have to calculate 33.33 % of 666 then we can get that by dividing 666 by 3 i.e. 222. Similarly if we have to calculate 16.67 % of 666, then we can simply get it by dividing it by 6 i.e. 111.

Important fractional equivalent of Percentages are listed below:

Fractional Equivalents of Percentages

Percentage to fraction

Examples of using Fractional Equivalent of Percentage:

Ex1: What is 28.56 % of 1428.

Solution: 28.56 % of 1428 = 2/7 of 1428 = 408.

Ex2: If 16.67 % of some value is 32. Calculate 37.5 % of that value?

Solution: 16.67 % (1/6) of X = 32 => X = 32 x 6

37.5 % of 32 x 6 = 3/8 of 32 x 6 = 3 x 4 x 6 = 72

Thus, we see that calculations become very easy once we adopt this technique.

Calculating Percentage Increase|Decrease: Percentage Increase/Decrease is required in many calculations. Using conventional way can be time taking. So here there is a simple way to calculate % increase/decrease. We can calculate % increase/decrease with the help of Multiplying Factors. Multiplying factors are those factors which can be multiplied to get the final % increase/decrease.

For example 10 % increase in 100 can be get by multiplying 1.1 to 100 = 110

Similarly 10 % decrease in 100 can be had by multiplying 0.9 to 100 = 90

10 % increase in 80 can be get by multiplying 1.1 to 80 = 88

Similarly 20 % decrease in 80 can be had by multiplying 0.8 to 80 = 64

Multiplying Factor & Multiplying Fraction for some Percentage Increase/Decrease are listed Below:

Multiplying Factor

More Examples of Calculating Percentage Increase|Decrease with Multiplying Factor:

Ex1:Cost price of an article is Rs 70. What should be the selling price to gain 20 % ?

Solution: Selling Price(SP) = Increase in 20 % of Cost Price (CP)

SP = 70 x 1.2 = Rs 84 (Ans).

Ex2: Ram’s monthly income is 20 % more than Mohan’s monthly income whose monthly income is 20 % less than Suresh. If Suresh monthly income is Rs. 15,000/-, calculate Ram’s monthly income.

Solution: The question can be solved easily with the trick below-

Suresh Income —–>Mohan’s Income ——>Ram’s Income

 15,000            15,000 x 0.8 = 12,000    12,000 x 1.2 = 14,400 (Ans.)

Ex3: Population of a town is 10,000. If it increased by 20 % in two consecutive years. Then it is decreased by 20 % in the third year. Find the population after 3 years.

Solution: The question can be solved easily with the help of Multiplying factor.

I Year ——->II Year ———->III Year —————–>IV Year

10000     10000 x 1.2     10000 x 1.2 x 1.2    10000 x 1.2 x 1.2 x 0.8 = 11520

Ex4: If in the above question, the initial value is not given then calculate % increase/decrease in population after 3 years.

Solution: Trick : We can calculate these types of % Increase/Decrease with the help of Multiplying factor assuming initial value as 100 OR 100x. By assuming initial value as 100, we can calculate the % Increase/Decrease by subtracting 100 from the final value.

I Year ——->II Year ————->III Year ————–>IV Year

100        100 x 1.2 = 120     120 x 1.2 = 144     144 x 0.8 = 115.2

Therefore % Increase = 115.2 – 100 = 15.2 % (Ans.)

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