Hope that previous
post on this topic has helped you in understanding the concept of this chapter “Percentage”.
Here in this post I am going to clear your concept regarding more various
frequently asked questions from one of the most important Chapter “Percentage”
which will help you to face these problems with full confidence and solve them
in just 30 seconds mentally or with a little calculations.
The work of
shortening the procedure is to be done by the student depending on his calibre
and speed as in this post I am going to elaborate each and every concept in
very detail manner with the help of you will be able to understand and solve
the problems of this self.
Let’s
continue with this chapter............
Question Type 3rd :- (Questions Based on Election)
Q1. In an
election between two candidates one of them gets 41% of votes and is rejected
by a majority of 2412 votes. Find the number of votes drawn in the elections.
Sol. In these question student should always
understand that whatever the voting was held in the election but the total
votes which are drawn in the election are always considered as 100% votes. When
the number of candidates is two and one of them gets 41% then the votes of the
second candidate will be (100% - 41% = 59%) : -
Let the
total votes drawn in the election are x then,
1st Candidate got votes = 41% of x.
2nd Candidate got votes = 59% of x.
According to the concept of these questions
the difference between these two percentage values will be equal to the
difference of votes given in the questions and the equation will be
59% of x – 41% of x = 2412
18% of x = 2412
x =
(2412 × 100) /18 (simplify it.)
x
= 13400 votes.
Question Type 4th :- (Questions
Based on Population/Price/Any commodity Percentage increase or decrease)
Concept
If the present population of
a town is x and it increases by p% on the first year and decreases by q% in
the second year while again increases by r% in the third year then the
population of the town after 3 years will be –
Population after 3 years = x × {(100
+ p) / 100)} × {(100 - q) / 100} × {(100 + r) / 100}
|
Q2. The population
of a town is 10,000. It increases by 10% during 1st year, while
decreases by 20% during 2nd year and again increases by 30% during
the 3rd year. What will be the population of the town after 3 years.
Sol. 1st
Method :- Present Population = 10,000
Increase
during 1st year = 10% of 10000 = 1000
Population
after 1st year = 10000 + 1000 = 11000
Decrease during
2nd year = 20% of 11000 = 2200
Population
after 2nd year = 11000 - 2200
= 8800
Increase during 3rd
year = 30% of 8800 = 2640
Population
after 3rd year = 8800 + 2640
= 11440
2nd Method :- (One line
Calculation)
Required Population = 10000 × {(100
+ 10)/100} × {(100 – 20)/100} × {(100 + 30)/100}
= 10000 ×
(110/100) × (80/100) × (130/100) (Simplify it)
= 11440
Q3. The
population of a town is 8000. If the number of males increases by 6% and number
of females increases by 10% then the population will be 8600. Find the number
of males presently present in the town.
Sol. I will
show you two conceptual methods of solving these types of questions. Let’s see
them.
1st Method :- According to the question the population of
the town is 8000. Let the number of male in the town is x therefore the number
of female will be (8000 - x) Now
Present
Population = 8000
Number of
men in the population = x which increases by 6% &
Number of
females in the population = (8000 - x) which increases by 10%
After
increases the new population will be = 8600.
Now
Equation will be :- x × {(100 + 6)/100}
+ (8000 - x) × {(100 + 10)/100} = 8600.
x ×
(106/100) + (8000 - x) × (110/100) = 8600
106x + 880000 –
110x = 860000
4x
= 20000
x = 5000.
Hence the required number of
males = 5000.
Method 2nd
:- (Alligation Method)
Present population = 8000
The would be
population after increase = 8600.
Population increase
= 600.
The overall percentage increase
in the population will be = (600/8000) × 100
=
(15/2)%
(Always
keep this simplification in fraction not in decimal otherwise it may go wrong)
Males
females
6%
10%
(15/2)%
(10 –
15/2)%
(15/2 - 6)%
(5/2)%
(3/2)%
On simplifying we get the ratio between
number of men & females in the town as 5:3
Now
number of males = (5/5+3) × 8000
= (5/8) × 8000
number of males = 5000.
Note you may say that this is so
long but dear this is the only way to explain the whole concept of the question
to you now its upto you that how fast and short handedly you can solve these
type of questions)
More types
of questions will be followed soon on this blog........................
No comments:
Post a Comment