# IPM Indore 2022: Basic Concepts of Percentages

By Vijeta Bhatt|Updated : July 30th, 2021

Read here basic concepts and tips to solve Percentage question for BBA and HM exams. Must read this Article and know Tips & Tricks to solve Percentage questions.

'Percentage' is a very important concept, applicable in almost all the topics of Quantitative Techniques. To help you all score better in the various BBA & HM Entrance exams, we are sharing some important concepts and shortcut tricks that will help you to solve questions based on percentages easily and within less time.

### Percentage

• The percentage is per cent which means parts per hundred.

### Per cent sign

• The per cent sign is the symbol: %
• It is written to the right side of the number: 50%

### Percentage Definition

• The percentage is a value that represents the proportion of one number to another number.
• One per cent represents 1/100 fraction.

If we have to convert the percentage into a fraction then it is divided by 100.

Let's understand the concepts of the Percentage in detail:

### 1.0 Concept - One

1. A + B + AB/100 When A and B both are a positive change.
2. A – B – AB/100 When A is a positive change and B is a negative change.
3. – A + B – AB/100 When A is a negative change and B is a positive change.
4. – A – B + AB/100 When A and B both are a negative change.

Important: There is no need to remember the above formulas, you have to just remember:

•  ± A ± B ± AB/100 and put the sign of change, if negative, then (-) and positive then, (+) but keep in mind that sign of AB is the product of signs of A and B.

Example1: The price of a book is reduced by 10% and the sale of the book is increased by 15%. Find the net effect on revenue.

Example 2: If the length and breadth of a rectangle are increased by 5% and 8% respectively. Find the % change in the area of the rectangle.

### 2.0 Concept - Two

New solution × new % = old solution × old %
This formula is applicable for the commodity which is constant in the solution or mixture, its quantity doesn’t change after mixing in solution.

Example 3:  A mixture of sand and water contains 20% sand by weight. Of it, 12 kg of water is evaporated and the mixture now contains 30% sand.
(a) Find the original mixture.
(b) Find the quantity of sand and water in the original mixture.

Solution: In this sand is constant in the mixture. So we will apply this formula on the sand, not on the water.
(a) Let the original mixture is P kg, So new mixture = (P-12) kg
old% = 20 and new % = 30
new solution × new % = old solution × old %
(P-12)× 30% = P × 20%
3P – 36 = 2P
P = 36 Kg.
(b) Quantity of sand in original mixture = 20% of 36 = 7.2 Kg
Quantity of water in original mixture = 80% 0f 36 = 28.8 Kg
Or, Quantity of mixture – quantity of sand = 36 -7.2 = 28.8 Kg

Example 4: 30 litres of a mixture of alcohol and water contains 20% alcohol. How many litres of water must be added to make the alcohol 15% in the new mixture?

Solution: only water is added to the mixture so, there is no change in alcohol. We will apply the above formula to alcohol. Let water added is P litres.
Old mixture = 30 litres, old % of alcohol = 20%
New mixture = 30+P litres, new % of alcohol = 15
using, new solution × new % = old solution × old %
(30+P) × 15% = 30 × 20%
P = 10 litres, hence 10 litres of water is added.

### 3.0 Concept - Three

Example 5: If the price of milk increased by 25%, by how much per cent must Rahul decrease his consumption, so as his expenditure remains the same.

Solution: Let the price of milk is 20 Rs/ litre and Rahul consumes 1-litre milk.
Expenditure of Rahul = price × consumption
Now the price of milk is increased by 25%, so the new price is (125/100)× 20 = Rs. 25
but his expenditure remains the same
So, new consumption × new price = old price × old consumption
new consumption × 25 = 20 × old consumption
new consumption  =(20/25)  × old consumption
new consumption % = (20/25)× old consumption × 100
new consumption % = 80% of old consumption
decrease in consumption = 20 %
Using the above trick:  Given, price % is increased so the sign will be (+) and consumption % will decrease.
Decrease in consumption =(25/125) × 100 = 20%

Example 6: If the price of milk decreased by 25%, by how much per cent must Rahul increase his consumption, so as his expenditure remains the same.

Solution: Let the price of milk is 20 Rs/ litre and Rahul consumes 1-litre milk.
Expenditure of Rahul = price × consumption
Now the price of milk is decreased by 25%, so the new price is (75/100)× 20 = 15 Rs.
but his expenditure remains the same
So, new consumption × new price = old price × old consumption
new consumption × 15 = 20 × old consumption
new consumption  =  (20/15)× old consumption
new consumption % = (20/15)× old consumption × 100
new consumption % = 133(1/3)% of old consumption
increase in consumption = 33(1/3) %

Using the above trick: given price, % is decreased so the sign will be (-) and consumption % will increase.
Increase in consumption = (25/75) x  100 = 33(1/3)%

### 4.0 Concept - Four

Example 7: The population of a town is 6000. It increases 10% during the 1st year, increases 25% during the 2nd year and then again decreases by 10% during the 3rd year. What is the population after 3 years?

Example 8: The population of a village increases by 10% during the first year, decreased by 12% during the 2nd year and again decreased by 15% during the 3rd year. If the population at the end of the 3rd year is 2057.

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