CAT and Other MBA Exams: Study Notes || QA || PERCENTAGES

PERCENTAGE FOR COMPARISON:

Percentage helps us to compare between different fractions when the denominator or the total number is different in each case. It is one of the simplest tools for the comparison of data.

Take for example, this table below which shows the marks obtained by a student in 3 different subjects

From this data alone, we cannot compare the marks obtained for the various subjects.

Now suppose we have the data of the total marks obtained as follows

Now as all the three subjects are represented on a scale of 100, it is easy to compare the marks for the three subjects and decide which subject has the student scored the maximum in.

1.1.2) REPRESENTATIONS OF PERCENTAGES

CONVERSIONS

1) To convert a fraction into a percentage

🡪 Multiply and divide by 100. 

🡪 Keep the denominator as 100, the numerator you obtain is the required answer.

ILLUSTRATION:

1. Recently I went to buy a laptop for myself. The dealer said that he has laptops of two companies: HP and Lenevo. He was selling the HP laptop for Rs. 42000 and told me that he will offer me the same at 78 of that price while the Lenevo laptop was for Rs. 46000 and he was offering it at 4/5 of that price. I decided to buy the laptop on which I was getting a better percentage discount. Which one should I buy?
   Solution:

CONCEPT OF CHANGE

There are two types of change

1. Absolute value change:- It is the actual change in the quantity. For example, if there are 10 rabbits in the first year and 15 rabbits in the second year, the absolute change in the number of rabbits is 5
2. Percentage change:- This can be obtained by calculating the absolute change and dividing it by the initial number of rabbits present

PERCENTAGE CHANGE AND PERCENTAGE POINT CHANGE

 If the pass percentage of a class was 75 % in 1991 and 85% in 1992, we can calculate the percentage point change and the percentage change as follows

Percentage point change = Final percentage – Initial percentage= 85 %– 75% = 10 percentage points

TO INCREASE A NUMBER BY A GIVEN PERCENT

TO DECREASE A NUMBER BY A GIVEN PERCENT

TO FIND THE PERCENTAGE INCREASE OR DECREASE OF A GIVEN NUMBER, WE USE THE CONCEPT OF PERCENTAGE CHANGE AS EXPLAINED ABOVE

ILLUSTRATION:

1. In the IPL match an analysis was done for the two openers of both teams: Delhi Daredevils (DD) and Deccan Chargers (DC). It was found that the two DC openers Gilchrist and Gibbs together scored 20% more than what the two DD openers Sehwag and Gambhir scored. Gambhir scored 30 and Gibbs scored 40.  How much percentage less/more did Sehwag score than Gilchrist if Gilchrist scored 80?

Solution:

BASIC FORMULA

ILLUSTRATIONS:

1. Anil is taking an examination which has two sections A and B. He starts with section A and when he proceeds to section B he realizes that the marks carried for each question has decreased by 40% as compared to section A. How many more questions (in percentage) should he solve in section B as compared to section A if he wants to score same marks in section A and section B? Given that both sections carry equal marks. 

Solution: 

1. The petrol prices shot up by 20% due to Iraq War. Amit travels 2000 kms every month and his car gives a mileage of 20 kms per liter. By how many kilometers should he reduce his travel to maintain his expenditure to the previous level.

Solution:

1. After receiving two successive pay hikes if Ashish’s salary becomes 158 of his initial salary. By how much percent was the salary raised the first time if the second raise was twice as high (in %) as the first?
2. a) 15 %                  
   b) 20%                  
   c) 25%               
   d) 30%

Solution:

We can solve this question using two approaches:

Approach 1: (conventional)

Approach 2: (Recommended)

PERCENTAGE EQUIVALENCE TABLE

It’s good to know the reciprocals of numbers till 20. Once the reciprocals are known, the value of several fractions can be easily obtained from the table                                

                                                                                                                              Rows

Application of the table

Initially, it may take time to get used to the conversion, but after repeated practice, it saves a lot of time for calculation and can be one of your best time-saving strategies for the exam.

More applications of the Percentage Equivalence Table will be discussed in Class 

Constant Product Rule-Introduction

This rule can be used when there is a relationship or inverse proportionality between two parameters, i.e. when the product of two parameters is a constant. This concept can be applied to many arithmetic topics based on percentages like Time and Work, Time Speed Distance, Interest and Profit & Loss to just name a few

For example,

In the third example, if the price of a commodity is increased by a particular percentage, then to keep the “Expenditure”, which is the product of Price and Consumption constant, we need to reduce Consumption by a particular percentage. 

So the rule states that,

Also

Using this concept, we can draw a table for the change in component Q reflected due to a change in component P, when their product is constant, i.e when P and Q are inversely proportional.

SOME APPLICATIONS OF CONSTANT PRODUCT RULE:

1) Price of sugar is going up by 20%. Find the percentage reduction in consumption a family should adopt so that the expenditure remains a constant?

Solution:

2) Normally A does a certain work. But A is absent so Ravi has two options: B or C. B can finish the work by taking 6 hrs more than A while C is 1.5 times more efficient than B and can finish the work 4 hrs earlier than A. Find the usual time taken by A.

3) An architect is planning to increase the length of a rectangular room by 10% without increasing the area of the room. By what percentage must he reduce the breadth of the room?

.

4)Efficiency of A is 33.33% more than that of B. B takes 24 days to complete a work. How many days A will take to complete the work?

5)24 men can finish a work in 25 days. In how many days will 30 men finish the work?

Here (number of men) x  (number of days) = man days( constant)

By increasing the number of men by 25 %, time saved will be 20 %. So 30 men will take 20 days to finish the work.

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