**Percentages are special types of fractions in which the denominator is always hundred.**

**e.g.**

**It is written as 10% or its simplified form is**

**Percentage Increase/Decrease:**

**If the price of a commodity increases by a%, then the reduction in consumption so as not to increase the expenditure is:**

**If the price of a commodity decreases by a%, then the increase in consumption so as not to decrease the expenditure is:**

**Results on Population:**

**Populations after n year**=

**Populations before n years**=

**If the value of a number is first increased by a% and later decreased by a%. then the net effect is always decreased which is equal to a% of a and is written is**

**SOME IMPORTANT FRACTION VALUES :-**

**= 100 %**

**= 50 %**

**= 3 %**

**= 25 %**

**= 20 %**

**= 16 %**

**= 14 %**

**= 12 %**

**= 1 %**

**= 10 %**

**= 9 %**

**= 8 %**

**EX: A's income is 10% more than B's income. How much per cent is B's income less than A's income?**

**Sol:**Let B's Income = Rs. 100

A's income = = Rs. 110

Required percentage = %

= 9 %

**Ex: In an examination, 35% is passing marks one candidate obtain 135 marks and failed by 40 marks then find the maximum marks?**

**Sol:**35% = 135 + 40

100% =

= 500

**Ex: Rohit obtained 480 marks out of 600 and Mohit obtained 560 marks out of 800. Whose performance is better and how much %?**

**Sol:**

Rohit got = x 100 = 80 %

Mohit got = x 100 = 70 %

Rohit performance is better.

% better = x 100 = 14 %

**Ex: In an election between two candidates, 65 votes were declared invalid one candidate gets 52% votes and win by 98 votes.Find the total number of votes?**

Winner 52% Looser 48%

4% = 98

100% = 2450

Valid vote = 2450

Total vote = 2450 +65 = 2515

**Ex: The length and breadth of the rectangle are increased by 30% and 20% respectively, so find the net % change in its area?**

**Sol:**

Net % change = x + y +

= 30 + 20 +

= 56%

**Ex: A number is mistakenly divided by 10 instead of being multiplied by 10.What is the percentage error in the result?**

**Sol:**

Let the number is 10.

Actual result = 10 x 10 = 100

Wrong result = = 1

% change = x 100 = 99%

**Ex: The numerator of a fraction is increased by 400% and the denominator is increased by 500%, so the resultant fraction is 15/22. Find the original fraction?**

**Sol:**

=

=

Original Fraction =

Original Fraction =

**Ex: A, B and C are three persons. A earned 40% more than B and B earned 20% less than C, so what % more earned A than C.**

**Sol:**

A B C

112 80 100

A more earned than C = 112 – 100 = 12

= 12 %

**Ex: Due to reduction of 20% in the price of apples enables a person to purchase 16 apples more for Rs.320, so find the reduced rate of 10 apples?**

**Sol:**

Reduced rate = = 64

Reduced rate of 1 apple =

= Rs. 4

Reduced rate of 10 apples = 4 x10

= Rs.40

**Ex: A mixture of 40 litres of milk and water contains 10% water. How much water should be added, so water may be 20% in the new mixture?**

**Sol:**

40 4 lit.

80% = 36

1% =

20% =

= 9 Lit.

req. water = 9 – 4

= 5 lit.

**Ex: Fresh fruit contains 68% water and dry fruit contains 20% water. How much dry fruit can be obtained from 100 kg. of fresh fruit ?**

**Sol:**

fruit content in 100 kg. of fresh fruits = 100

= 32 kg.

Since , dry fruits contain 80% fruit content,

80% = 32

1% =

100% =

= 40 kg.

**Ex: In an examination, 35% of the candidates failed in Mathematics and 38% failed in English. 28% passed in both subjects, then how much percent failed in both the subjects?**

**Sol:**Failed in Maths = 35%

Passed in Maths = 100% 35% = 65%

Failed in English = 38%

Passed in Maths = 100% 38% = 62%

Failed in both subjects = 100% – (37%+28%+34%)

= 1%