Percentage in aptitude

1. Percentage
Introduction
Logic/ Concept/
Shortcuts
Real
life
Implementation
Examples

2. Introduction
How to find 43% of 1500?
43
100
X 1500 = 645
43% 0.43
43
100
315
1500
X 100 = 21%
How to find what is the
percentage of 315 on 1500?
43%
10% 10% 10% 10% 1% 1% 1%
150 X 4
600
15 X 3
45
+
645 =

3. Introduction
45% of a number is 15 less than 3/5th of the same number. Then
what is the number?
X
45
100
𝑋 X
3
5
𝑋
= 5km + 500 m = 5500 m or 5.5km
60% - 45% = 15
- 15
X = 100

4. Example
A candidate who gets 25% of the total marks in an exam fails by 32
marks. Another candidate who gets 37% of the total marks, gets 52
marks more than the required pass mark. The maximum marks in the
exam are which of the following?
x X
25
100
( ) x X
37
100
( ) - 52
=
x X
25
100
( )
32 + 52 x X
37
100
( )-
=
84
12 𝑥
100
=
8400 12 𝑥
=
700 𝑥
=
+ 32

5. Example
A candidate who gets 25% of the total marks in an exam fails by 32
marks. Another candidate who gets 37% of the total marks, gets 52
marks more than the required pass mark. The maximum marks in the
exam are which of the following?
37%
pass
mark
25%
32 52
84
12%
So, 12% = 84 marks
1% = 7 marks
Then 100 % will be 700 marks
Or X 100
100%
0%
(
84
12
) = 700 Marks

6. Introduction
In an election between two candidates, one got 55% of the total valid votes,
20% of the votes were invalid. The candidate is rejected by a margin of 7500
votes , the number of total voters is?
55% 45%
10%
10% = 7500
100%=75000
100%
80%=75000
100%= (75000/80)x100=93750

7. Logic
Say I got my salary, I’ve spent 30% of the salary in car, 20% of the
salary in bike and 10% of the salary in food. Then what % of
salary will be remaining?
30% + 20% + 10% = 60%
I’ve spent 30% of the salary in car, 20% of the remaining amount
in bike and 10% of the remaining amount in food. Then what %
of salary will be remaining?
100%
70%
56%
50.4%
- 30%
- 20% ( 20% of 70 = 14 )
So, -14
- 10% ( 10% of 56 = 5.6 )
So, -5.6
Remaining salary will be 40%

8. Example
A man bought a mobile phone for 40% of his salary. Then he also
spent 20% of the remaining amount in his car and half of the amount
now left as rent and the remaining amount is Rs.12000. Then what is
his salary?
100%
60%
48%
24%
- 40%
- 20% ( 20% of 60 = 12 )
So, -12
- 50% ( 50% of 48 = 24 )
So, -24
Remaining salary
So, 24% = 12000
Then 1 % will be
12000
24
______ X 100 = 50,000

9. A man = x no.s apples
7 toll gates
• Half of no. of apples and a half apple
7th (0) apple left

10. 127
63.5
1st
63
31.5
2nd
31
15.5
3rd
15
7.5
4th
7
3.5
5th
3
1.5
6th
1
0.5
7th
0
1. Half of the number of apples
2. Half apple

11. Example
A man bought a mobile phone for 40% of his salary. Then he also
spent 20% of the remaining amount in his car and half of the amount
now left as rent and the remaining amount is Rs.12000. Then what is
his salary?
50,000
30,000
24,000
12,000
80% of the previous amount
Then the previous amount is
Double
(24000/80)X 100 = 30,000
60% of the previous amount
Then the previous amount is
(30000/60)X 100 = 50,000
S X (
60
100
) 𝑋(
80
100
) 𝑋(
50
100
)= 12,000/-
S = 50,000/-

12. Logic
For example,
A man’s salary is 100 Rs
• And it is increased by 10 Rs,
• Then his salary becomes 110 Rs
• Then his salary is decreased by 10 Rs,
• Then is comes back to 100 Rs
A man’s salary is 100 Rs
• And it is increased by 10%,
• Then his salary becomes 110 Rs
• Then his salary is decreased by 10%,
• Then is comes back to 99 Rs

13. Example
When a number is increased by 23% the number becomes 2583.
Then what is the number?
100% 23%
+
123%
So, here 2583 is 123% of the number
Then 100% of the number is,
2583
123
_____ X 100 = 2100

14. Example
When a number is dec by 23% the number becomes 2583.
Then what is the number?
100% 23%
-
77%
So, here 2583 is 77% of the number
Then 100% of the number is,
2583
77
_____ X 100 = 3355

15. Example
When you bought a mobile from my shop, I got a profit of 23%. The
Selling price of the phone is Rs.2583/-. Then what is the Cost price?
100% 23%
+
123%
So, here 2583 is 123% of the number
Then 100% of the number is,
2583
123
_____ X 100 = 2100
𝑆𝑃
100+𝑃%
𝑋100 = CP
𝑆𝑃
100−𝐿%
𝑋100 = CP

16. Example
When a number is increased by 23% the number becomes 2583.
Then what is the number?
100% 23%
+
123%
So, here 2583 is 123% of the number
Then 100% of the number is,
2583
123
_____ X 100 = 2100
𝑆𝑃
100 + 𝑃%
𝑋 100 = 𝐶𝑃
𝑆𝑃
100−𝐿%
X 100 = CP

17. Logic
CI= P 1 +
𝑅
100
𝑛
CI= P 1 +
𝑅
100
2
1 +
𝑅 1/2
100
CI= P 1 +
𝑅/2
100
2𝑛
CI= P 1 +
𝑅/4
100
4𝑛
CI= P 1 +
𝑅1
100
1 +
𝑅2
100
Compound interest formulas:
If the time is 2 ½ years:
If its compounded half yearly
If its compounded quarter yearly
If its different rate of interest every time

18. Logic ( Compound Interest )
P = 1000 Rs. Rate = 10% per annum
Principal Interest
1000
1.
Year
100
1100
2. 110
1210
3. 121
1331
4.
110%
100% 10%
+
100% 10%
+
100% 10%
+
110%
110%
1000 𝑋
110
100
𝑋
110
100
𝑋
110
100
Compound Interest
For, 2 ½ years
1000 𝑋
110
100
𝑋
110
100
𝑋
105
100
For, half year calculation
1000 𝑋
105
100
( )
6
For, quarter year calculation
1000 𝑋
102.5
100
( )
12
1000 𝑋
110
100
𝑋
120
100
𝑋
130
100
For, different rate of interest every time
1st year= 10% 2nd year= 20% 3rd year= 30%

19. Logic
CI= P 1 +
𝑅
100
𝑛
CI= P 1 +
𝑅
100
2
1 +
𝑅 1/2
100
CI= P 1 +
𝑅/2
100
2𝑛
CI= P 1 +
𝑅/4
100
4𝑛
CI= P 1 +
𝑅1
100
1 +
𝑅2
100
Compound
Interest Formulas:
If the time is 2 ½ years:
If its compounded half yearly
If its compounded quarter yearly
If its different rate of interest every time
1000 𝑋
110
100
𝑋
110
100
𝑋
110
100
Compound Interest
For, 2 ½ years
1000 𝑋
110
100
𝑋
110
100
𝑋
105
100
For, half year calculation
1000 𝑋
105
100
( )
6
For, quarter year calculation
1000 𝑋
102.5
100
( )
12
1000 𝑋
110
100
𝑋
120
100
𝑋
120
100
For, different rate of interest every time
1st year= 10% 2nd year= 20% 3rd year= 30%

20. Example
Population of a city is increased by 20% every year. The
current population of the city is 2,00,000. Then what is the
population of the city after 3 years?
2,00,000 𝑿
𝟏𝟐𝟎
𝟏𝟎𝟎
𝑿
𝟏𝟐𝟎
𝟏𝟎𝟎
𝑿
𝟏𝟐𝟎
𝟏𝟎𝟎
= 3,45,600
12,00,000 𝑿
𝟖𝟓
𝟏𝟎𝟎
𝑿
𝟖𝟓
𝟏𝟎𝟎
𝑿
𝟖𝟓
𝟏𝟎𝟎
= Rs. 7,36,950/-
A cars value is depreciated by 15% every year. The new car
value is Rs. 12,00,000/-. Then what is the value of the car after
3 years?

21. A 100 liters container is filled with milk. 10 liters from
the container is replaced by water, and this iteration is
repeated for 2 more times. Then what is the quantity of milk
in the container?
100 liters
90
liters
Milk
10
liters
water
Milk water ratio 9 : 1
10
liters
Milk water ratio 9 : 1
Milk
9 ltrs
Water
1 ltr
81
liters
Milk
9
liters
water
10
liters
milk
1
Milk water ratio 81 : 19
10
liters
Milk water ratio 81 : 19
10 liters
Is divided
in the ratio
81:19
So, 8.1 : 1.9
72.9
liters
Milk
17.1
liters
water
72.9
liters
Milk
27.1
liters
water
+ 10 liters
Iteration 2
Iteration 3
Iteration 1
So, remaining milk in the
container is 72.9 liters

22. A 100 liters container is filled with milk. 10 liters from
the container is replaced by water, and this iteration is
repeated for 2 more times. Then what is the quantity of milk
in the container?
100 liters
90
liters
Milk
10
liters
water
81
liters
Milk
19
liters
water
72.9
liters
Milk
27.1
liters
water
10 liters is going out
(ie) 10% from the container is gone out.
So, remaining will be 90% in the container.
90% of
100 is 90
90% of
90 is 81
90% of
81 is 72.9
So the simple solution for this problem is
finding 90% of 90% of 90% of 100.
That is 100 x
90
100
x
90
100
x
90
100
= 72.9
Remaining milk in the container will be
72.9 liters

23. Example
In an exam 60 % of the boys and 70 % of the girls who appeared
passed.42 girls passed the exam and this number is 25 % of the
number of boys who failed in the exam. How many students (boys
and girls) appeared for the exam?
70% of girls = 42
Then, 100% of girls =
So, total number of girls = 60
X100
𝟒𝟐
𝟕𝟎
= 60
25% of boys failed = 42
Then, 100% of boys failed =
So, total number of who failed is = 168
Which is 40% of boys
X 100
𝟒𝟐
𝟐𝟓
= 168
Then 100% of boys =
X100
𝟏𝟔𝟖
𝟒𝟎
= 420
60 girls + 420 boys
= 480 students

24. Introduction
The price of a commodity increases by 25%. By what % should the
consumption be reduced to keep the expenditure constant?

25. Introduction
There are 100 people in an auditorium, out of which 99% are male. How
many men we have to remove to make the percentage of men as 98%?
Male 99% = 99
Female 1%= 1
____________
Male 98% = 49
Female 2% = 1
𝟗𝟗 − 𝒙
𝟏𝟎𝟎 − 𝒙
𝑿 𝟏𝟎𝟎 = 𝟗𝟖%
X=50