Aptitude Concepts of Percentages and its Important Shortcuts

Concepts of Percentages and its Important Shortcuts

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

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

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

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

Important: There is no need to remember 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 product of signs of A and B.

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

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

Concept 2:

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. 

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 sand not on 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 much litre of water must be added to make the alcohol 15% in the new mixture?

Solution: only water is added in the mixture so, there is no change in alcohol. We will apply 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 same.

Solution: Let 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 new price is (125/100)× 20 = 25 Rs.
but his expenditure remains 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 above trick:  Given, price % is increased so sign will be (+) and consumption % will decrease.

Decrease in consumption =(25/125) × 100 = 20%

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

Solution: Let price of milk is 20 Rs/litre  and Rahul consumes 1 litre milk.

Expenditure of Rahul = price × consumption 

Now price of milk is decreased by 25%, so new price is × 20 = 15 Rs.

but his expenditure remains 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 above trick: given price % is decreased so 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 1^styear, increases 25% during 2^nd year and then again decreases by 10% during 3^rd year. What is the population after 3 year.

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