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# Important Notes : Percentage

Mahendra Guru : Online Videos For Govt. Exams

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%