Percentage – The Foundation of Arithmetic

Percentage is one of the most important topics in competitive examinations. It acts as the foundation for many other chapters such as:

• Profit and Loss
• Simple Interest
• Compound Interest
• Discount
• Ratio and Proportion
• Partnership
• Data Interpretation
• Average
• Mixture and Allegation

A student who understands Percentage properly rarely struggles in arithmetic.

For JKSSB examinations, percentage questions are frequently asked directly as well as indirectly through other arithmetic topics.

Free Mcqs for percentage

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What is Percentage?

The word Percentage means:

"Per Hundred"

The symbol of percentage is %.

If we say:

25%

It means:

25/100

Similarly:

Percentage	Fraction
10%	10/100 = 1/10
20%	20/100 = 1/5
25%	25/100 = 1/4
50%	50/100 = 1/2
75%	75/100 = 3/4
100%	1

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Why Percentage is Important?

Suppose a student scores 72 marks out of 90.

Instead of writing:

72/90

we convert it into a percentage:

7290×100\frac{72}{90}\times1009072​×100

= 80%

This allows easy comparison.

For example:

Student	Marks Obtained	Total Marks	Percentage
A	72	90	80%
B	160	200	80%

Even though marks differ, both performed equally.

This is why percentage is widely used in:

• Exams
• Elections
• Economics
• Banking
• Statistics
• Population studies
• Government reports

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Basic Formula of Percentage

Formula 1

Percentage

Percentage=value/total​×100

Example

A student gets 45 marks out of 60.

4560×100\frac{45}{60}\times1006045​×100 =75%=75\%=75%

Answer = 75%

like this question

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Formula 2

Finding Value

Value=Percentage×Total100Value=\frac{Percentage\times Total}{100}Value=100Percentage×Total​

Example

What is 20% of 500?

=20×500100=\frac{20\times500}{100}=10020×500​ =100=100=100

Answer = 100

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Formula 3

Finding Total

Total=Value×100PercentageTotal=\frac{Value\times100}{Percentage}Total=PercentageValue×100​

Example

25 is 20% of a number.

Find the number.

Number=25×10020Number=\frac{25\times100}{20}Number=2025×100​ =125=125=125

Answer = 125

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Percentage, Fraction and Decimal Conversion

This is one of the most important JKSSB revision tables.

Must Memorize Table

Percentage	Fraction	Decimal
1%	1/100	0.01
5%	1/20	0.05
10%	1/10	0.1
12.5%	1/8	0.125
20%	1/5	0.2
25%	1/4	0.25
33.33%	1/3	0.333
40%	2/5	0.4
50%	1/2	0.5
60%	3/5	0.6
66.67%	2/3	0.667
75%	3/4	0.75
80%	4/5	0.8
90%	9/10	0.9
100%	1	1

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Students Often Confuse

Concept	Meaning
20% of 50	20/100 × 50
50% of 20	50/100 × 20
Percentage of a number	Part from whole
Percentage increase	Growth from original value
Percentage decrease	Reduction from original value

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Finding Percentage of a Quantity

Example 1

Find 30% of 200.

=30100×200=\frac{30}{100}\times200=10030​×200 =60=60=60

Answer = 60

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Example 2

Find 12.5% of 160.

12.5% = 1/8

160×18160\times \frac18160×81​

=20

Answer = 20

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Percentage Increase

This area is extremely important in JKSSB, SSC and Banking exams.

Formula

Percentage Increase=IncreaseOriginal Value×100Percentage\ Increase= \frac{Increase}{Original\ Value} \times100Percentage Increase=Original ValueIncrease​×100

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Example

Salary increased from ₹4000 to ₹5000.

Increase:

5000−4000=10005000-4000=10005000−4000=1000 10004000×100\frac{1000}{4000}\times10040001000​×100

=25%

Answer = 25%

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Percentage Decrease

Formula

Percentage Decrease=DecreaseOriginal Value×100Percentage\ Decrease= \frac{Decrease}{Original\ Value} \times100Percentage Decrease=Original ValueDecrease​×100

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Example

Population decreases from 5000 to 4000.

Decrease:

5000−4000=10005000-4000=10005000−4000=1000 10005000×100\frac{1000}{5000}\times10050001000​×100

=20%

Answer = 20%

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Shortcut Percentage Calculation

Competitive exams often require fast calculations.

10%

Move decimal one place left.

Number	10%
500	50
80	8
750	75

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5%

Half of 10%

Example:

5% of 400

10% = 40

5% = 20

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25%

¼ of the number

Example:

25% of 200

= 50

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50%

Half of the number

Example:

50% of 600

=300

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75%

3/4 of the number

Example:

75% of 400

=300

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Successive Percentage Change

Students frequently make mistakes here.

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Increase by 20% then Increase by 30%

Many students wrongly add:

20% + 30% = 50%

Wrong.

Correct Formula:

Net Change=a+b+ab100Net\ Change= a+b+\frac{ab}{100}Net Change=a+b+100ab​

Where:

a = 20

b = 30

20+30+20×3010020+30+\frac{20\times30}{100}20+30+10020×30​ =56%=56\%=56%

Answer = 56% increase

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Quick Revision

Change	Net Result
+20%, +30%	+56%
+10%, +20%	+32%
+25%, +20%	+50%

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Increase Followed by Decrease

Formula

Net=a−b−ab100Net=a-b-\frac{ab}{100}Net=a−b−100ab​

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Example

Increase by 20%

Then decrease by 20%

20−20−20×2010020-20-\frac{20\times20}{100}20−20−10020×20​ =−4%=-4\%=−4%

Net decrease = 4%

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Important Exam Observation

Students think:

+20% and -20%

cancel each other.

This is WRONG.

Because percentages are applied on different bases.

This is a favorite examiner trap.

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Quick Concept Summary

Operation	Formula
Percentage	Value/Total ×100
Increase	Increase/Original ×100
Decrease	Decrease/Original ×100
Successive Increase	a+b+ab/100
Increase then Decrease	a-b-ab/100

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Percentage and Ratio Relationship

Very important for JKSSB.

If:

B is 20% more than A

Then:

B=120% of AB=120\% \ of \ AB=120% of A B:A=120:100B:A=120:100B:A=120:100 =6:5=6:5=6:5

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Common Conversions

Percentage	Ratio
20% increase	6:5
25% increase	5:4
50% increase	3:2
100% increase	2:1
20% decrease	4:5
25% decrease	3:4
50% decrease	1:2

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Percentage in Profit and Loss

Profit %

Profit%=ProfitCP×100Profit\%= \frac{Profit}{CP} \times100Profit%=CPProfit​×100

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Loss %

Loss%=LossCP×100Loss\%= \frac{Loss}{CP} \times100Loss%=CPLoss​×100

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Example

CP = ₹100

SP = ₹120

Profit = ₹20

20100×100\frac{20}{100}\times10010020​×100

=20%

Profit = 20%

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Percentage in Simple Interest

SI=P×R×T100SI=\frac{P\times R\times T}{100}SI=100P×R×T​

Here,

R = Rate Percentage

Example:

Principal = 1000

Rate = 10%

Time = 2 years

SI=1000×10×2100SI=\frac{1000\times10\times2}{100}SI=1001000×10×2​

=200

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Percentage in Population Questions

Population growth questions frequently use percentage.

Example:

Population = 10,000

Growth = 20%

New Population:

10000×12010010000\times\frac{120}{100}10000×100120​

=12,000

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One-Look Revision Table

Fraction	Percentage
1/2	50%
1/3	33.33%
1/4	25%
1/5	20%
1/6	16.67%
1/8	12.5%
3/4	75%
4/5	80%

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Memory Tricks

12.5%

Think:

18\frac1881​

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33.33%

Think:

13\frac1331​

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66.67%

Think:

23\frac2332​

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75%

Think:

34\frac3443​

These appear repeatedly in competitive exams.

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Most Asked JKSSB Facts

1. Percentage means per hundred.
2. Symbol is %.
3. 25% = 1/4.
4. 12.5% = 1/8.
5. Increase and decrease by same percentage never cancel.
6. Percentage forms the base of Profit-Loss and Interest chapters.
7. Fraction-percentage conversion is heavily tested.

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JKSSB Practice MCQs

MCQ 1

25% of 400 is:

A. 50

B. 75

C. 100

D. 125

Answer

C. 100

Explanation

25% = 1/4

400 ÷ 4 = 100

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MCQ 2

40 is what percent of 200?

A. 10%

B. 20%

C. 25%

D. 30%

Answer

B. 20%

Explanation

200/40​×100

=20%

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MCQ 3

A salary increases from ₹5000 to ₹6000. Percentage increase is:

A. 15%

B. 20%

C. 25%

D. 30%

Answer

B. 20%

Explanation

Increase = 1000

5000 /1000​×100

=20%

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MCQ 4

Increase by 20% and then decrease by 20%.

Net effect?

A. 0%

B. 2%

C. 4% decrease

D. 4% increase

Answer

C. 4% decrease

Explanation

20−20−10020×20​

=-4%

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MCQ 5

12.5% of 320 equals:

A. 20

B. 30

C. 40

D. 50

Answer

C. 40

Explanation

12.5% = 1/8

320 ÷ 8 = 40

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