**Concept 1**

1. A+B+AB/100 When A and B both are the positive change

2. A-B-AB/100 When A is positive change and B is a negative change

3. -A+B-AB/100 When A is negative change and B is a positive change.

4. -A-B+AB/100 When A and B both are the 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.

**Example2**: If the length and breadth of a rectangle are increased by 5% and 8% respectively. Find the % change in the area of the rectangle.

**Concept 2:**

**New solution × new % = old solution × old % **This formula is applicable to the commodity which is

**constant**in the solution or mixture, its quantity doesn’t change after mixing in solution.

**Example3:**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.

Solution: In this sand is constant in the mixture. So we will

**apply this formula on the sand, not on the water**.

(a)Find the original mixture.

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) Find the quantity of sand and water in the original mixture.

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 on 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.

**Concept 3:**

**Example 5**: If the price of milk increased by 25%, by how much percent 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 price of milk is increased by 25%, so the new price is (125/100)× 20 = 25 Rs.

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 decreases by 25%, by how much percent must Rahul increase his consumption, so as his expenditure remains the same.

Example 6:

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 × 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)%**

**Concept 4****:**

**Example 7:** The population of a town is 6000. It increases 10% during the 1^{st} year, increases 25% during the 2^{nd} year and then again decreases by 10% during the 3^{rd} 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 2^{nd} year and again decreased by 15% during the 3^{rd} year. If the population at the end of the 3^{rd} year is 2057.

**For Basics of Percentage, click the link given below - **

**Know the basics of Percentages**

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