Important Notes : Percentage

CONCEPT OF PERCENTAGE

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%