Here in
this post I am going to clear your concept regarding 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 1st :- (Basic
Percentage Questions)
Q1. Express
the following percentage as fraction:-
A
12.5% b. 75% c. 48% d. 225%
Sol. In these question student should divide the
percentage value by 100 and should reduce it in its simplest form. Example: -
A
12.5% = 12.5 /100 = 125/1000 (remove the decimal)
= 1/8 (After reducing it in the simplest
form)
B 75% = 75 / 100 = 3/4 (After reducing it in
the simplest form)
C 48% = 48/ 100 = 12/25 (After reducing it in the simplest form)
D 225% = 225/100 = 9/4 (After reducing it
in the simplest form)
= 2(1/4) (Converting it into mixed
fraction.)
Q2. Express the following fractions into
percentage :-
A 3/5 b. 1/3 c. 5/8
Sol. In these question student should multiply the
fraction value by 100 should simplify it dividing it. Example: -
A 3/5 = (3/5) × 100 = 3×20 = 60%
b 1/3 = (1/3) × 100 = 33.33%
c
5/8 = (5/8) × 100 = 5 × 12.5 = 62.5%
Question Type 2nd :- Comparison
Questions
Concept:-
x is what percent of y = (x/y)
× 100.
y is what percent of x = (y/x) × 100.
x is what percent more than y = { (x-y) / y }
× 100.
y is what percent more than
x = { (y-x) / x } × 100.
Note :- You always
get confused what should come in denominator, simple way to remember this
concept is that value which comes after “of”, “then”, “from” comes in the
denominator.
|
Q1. What
percent is number 6 of number 25?
Sol. As
explained in the concept :- (6/25) × 100 = 24%.
Q2. Manish
obtained 340 marks out of a maximum of 500 marks. Find the percentage of marks
obtained by him.
Sol. As explained in the concept :- (340/500) × 100 = 68%
Q3. Two numbers are 20% and 50% more than a third number.
What percentage is the first number of the second number.
Sol. Let the 3rd number be 100.
Then 1st
number = 120. & 2nd number = 150.
As
explained in the concept :- (1st number / 2nd number) ×
100 = (120/150) × 100 = 80%.
Q4. Two numbers are 30% and 40% less than a third number.
What percentage is the second number then the first number.
Sol. Let the 3rd number be 100.
Then 1st
number = 70. & 2nd number = 60.
As
explained in the concept :- (2nd number / 1st number) × 100 = (60/70) × 100 = 85.71%.
Q5. Two numbers are 20% and 25% of a third number. What
percentage is the first number of the second number.
Sol. Let the 3rd number be 100.
Then 1st
number = 20. & 2nd number = 25.
As
explained in the concept :- (1st number / 2nd number) ×
100 = (20/25) × 100 = 80%.
Q6. A man
expends 75% of his income. When his income increases by 20% then he also
increases his expenses by 10%. Find the percentage increase in his savings.
Sol. Let
the income of the man be Rs. 100/-
When he expends 75% means Rs. 75/- then
he saves Rs. 25/- only.
New income after 20% increase will be
Rs. 120/-
Then he increases 10% in his
expenditure means now he expends Rs. 75/- + Rs. 7.50/- = Rs. 82.50/- therefore
now his new saving will be Rs. (120 – 82.50 = 37.50)/-
Now
increase in his savings = 37.50 – 25 = Rs. 12.50/-
Hence we
can say that his saving increases Rs. 12.50/- from Rs. 25/-
As
explained in the concept :- % increase in his saving = (12.50/25) × 100 = 50%.
(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........................
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