Sunday, September 28, 2008

Percentage and its applications

Your competence with percentages and its application should form a very important part of your armory of CAT preparation or, for that matter, preparation for any other MBA exam. The concept of percentage will be applied in not only your quant section but also your data interpretation (DI) section. Therefore, master this important concept and make it your habit to calculate percentages mentally.

The word ‘percentage’ literally means ‘per hundred’ or ‘for every hundred.’ Therefore, whenever you calculate something as a part of 100, that part is numerically termed as percentage.

In other words, percentage is a ratio whose second term is equal to 100. For example, 1:4 can be written as 25: 100 or 25%, 3: 8 can be written as 37.5: 100 or 37.5%, 3: 2 can be written as 150: 100 or 150%, and so on.


Basic formula of percentage:

percentage formula

Percentage of:

percentage of formula

Percentage increase/decrease:

Percentage increase/decrease when a quantity a increase/decreases to become another quantity b is
percentage increase/ decrease

Percentage less than/greater than:

Have a look at the picture given below:

percentage greater than/ less than

You can see that Johnny is taller than Vicky. What will your answer be if I ask

(a) By what percentage is Johnny taller than Vicky?

(b) By what percentage is Vicky shorter than Johnny?


percentage greater than/ less than

conversion of fractions into percentages

Therefore, to find the final quantity after a 20% increase, we can directly multiply the old quantity by a factor of 1.2 and get the new quantity. Similarly, for a 20% decrease, we can multiply the old quantity by 0.8 and get the new quantity. The factors to be multiplied for various percentage increase/decrease are given below:

multiplication factors for percentage increase/ decrease

The biggest advantage of using the factors is that for subsequent percentage increase/decrease, we just keep on multiplying the corresponding factors and get the final quantity.


1. The performance bonus of a salesman increases by 10% in the first year, by 20% in the second year, and by 30% in the third year. What is the overall percentage increase in his bonus in 3 years?

Answers: Let the bonus at the start of the first year be Rs100.

Therefore, to find the final bonus we just multiply by factors.

Final bonus = 100 × 1.1 × 1.2 × 1.3 = 171.6.

Therefore, overall percentage increase = 71.6%

NOTE: note that taking initial value of 100 makes the problem simpler; whatever increase we get is directly equal to the percentage increase.

2. An amount was first reduced by 10% and then further reduced by 20% and Rs10 800 were left. What was the original amount?

Answer: Let the original amount be A.

Therefore A × 0.9 (factor for 10% decrease) × 0.8 (factor for 20% decrease) = 10 800

Or A = Rs15 000.


percentages solved problems

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