PERCENTAGE – COMPLETE NOTES WITH EXAMPLES For Class 5 JNVS

1. What is Percentage?

The word percentage comes from the Latin word “per centum” meaning per hundred.

👉 Percentage (%) = Value out of 100

Definition:

A percentage is a number or ratio expressed as a fraction of 100.

Examples:

• 50% = 50 out of 100 = 50/100 = 1/2
• 25% = 25/100 = 1/4
• 75% = 75/100 = 3/4

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2. Converting Fractions into Percentages

Formula:

$$\text{Percentage}=\left(\frac{\text{Fraction}}{1}\right)\times 100$$

Examples:

1. Convert 3/5 into percentage

$$\frac{3}{5}\times 100=60\mathrm{\%}$$

2. Convert 7/20 into percentage

$$\frac{7}{20}\times 100=35\mathrm{\%}$$

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3. Converting Decimal into Percentage

Formula:

$$\text{Decimal}\times 100=\text{Percentage}$$

Examples:

1. 0.45 = 45%
2. 0.125 = 12.5%
3. 1.2 = 120%

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4. Converting Percentage into Fraction or Decimal

Percentage to Fraction:

$$\frac{\text{Percentage}}{100}$$

Example:

• 40% = 40/100 = 2/5

Percentage to Decimal:

Divide percentage by 100.

Example:

• 18% = 0.18

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5. Finding Percentage of a Quantity

Formula:

$$\text{Required Value}=\frac{\text{Percentage}}{100}\times \text{Quantity}$$

Examples:

1. Find 20% of 250

$$\frac{20}{100}\times 250=50$$

2. Find 12% of ₹600

$$\frac{12}{100}\times 600=\text{₹}72$$

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6. Increase and Decrease Percentage

Examples:

1. Price of a book increases from ₹200 to ₹250
   Increase = 50

$$\frac{50}{200}\times 100=25\mathrm{\%}$$

2. Population decreases from 4000 to 3600
   Decrease = 400

$$\frac{400}{4000}\times 100=10\mathrm{\%}$$

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7. Successive Percentage Changes

When two percentage changes occur one after the other:

Formula:

$$\text{Net Change}=𝑥+𝑦+\frac{𝑥𝑦}{100}$$

(where x and y are percentage changes)

Example:

If a value increases by 20% and then by 10%:

$$20+10+\frac{20\times 10}{100}=32\mathrm{\%}\text{ increase}$$

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8. Percentage in Profit and Loss (Basic Idea)

• Profit % = (Profit / Cost Price) × 100
• Loss % = (Loss / Cost Price) × 100

Example: If CP = ₹500, SP = ₹600
Profit = 100
Profit % = (100/500) × 100 = 20%

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9. Percentage in Marks and Exams

Formula:

$$\text{Percentage of marks}=\frac{\text{Marks obtained}}{\text{Total marks}}\times 100$$

Example:

A student scores 360 out of 450.

$$\frac{360}{450}\times 100=80\mathrm{\%}$$

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10. Converting One Quantity to Another Using Percentage

Example:

20% of a number is 80. Find the number.

Let number = x

$$\frac{20}{100}\times 𝑥=80$$

$$𝑥=400$$

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11. Important Percentage Equivalents (Must Remember)

Percentage	Fraction
10%	1/10
12.5%	1/8
20%	1/5
25%	1/4
33⅓%	1/3
50%	1/2
75%	3/4

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12. Real‑Life Applications of Percentage

• Discounts in shops
• GST and tax calculations
• Exam results
• Population growth or decrease
• Profit and loss in business
• Interest in banks

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✅ SOLVED PRACTICE EXAMPLES

Example 1:

Find 35% of 840

$$\frac{35}{100}\times 840=294$$

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Example 2:

If the price of rice is reduced by 15% and now costs ₹510, find original price.

Let original price = x

$$0.85𝑥=510\Rightarrow 𝑥=\text{₹}600$$

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Example 3:

A number is increased by 10% and becomes 1100. Find the number.

$$1.1𝑥=1100\Rightarrow 𝑥=1000$$

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✍️ PRACTICE QUESTIONS

1. Find 18% of 750.
2. Convert 0.375 into percentage.
3. A shirt marked at ₹800 is sold at a discount of 20%. Find selling price.
4. The population of a town increases from 10,000 to 11,500. Find increase %.
5. If 25% of a number is 90, find the number.
6. A student gets 432 marks out of 600. Find percentage.
7. Price of goods decreases from ₹1200 to ₹1020. Find decrease %.
8. Increase ₹500 by 12%.
9. Reduce ₹900 by 10%.
10. What is 12.5% of 640?

📘 PERCENTAGE – MCQs FOR PRACTICE

🔹 LEVEL 1: BASIC CONCEPTS

1. What is 25% of 200?
A) 25
B) 40
C) 50
D) 60

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2. 0.35 expressed as a percentage is:
A) 3.5%
B) 30.5%
C) 35%
D) 350%

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3. Which of the following is equal to 20%?
A) 1/3
B) 1/4
C) 1/5
D) 1/10

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4. Convert 75% into fraction.
A) 1/4
B) 3/4
C) 2/3
D) 4/3

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5. What is 10% of 450?
A) 45
B) 40
C) 50
D) 55

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🔹 LEVEL 2: PERCENTAGE OF NUMBER

6. Find 18% of 600.
A) 90
B) 100
C) 108
D) 120

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7. 20% of a number is 80. The number is:
A) 200
B) 300
C) 400
D) 500

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8. 12.5% of 800 is:
A) 100
B) 80
C) 120
D) 150

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9. What is 45% of 360?
A) 162
B) 180
C) 150
D) 144

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10. If 30% of x is 150, then x is:
A) 300
B) 400
C) 500
D) 600

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🔹 LEVEL 3: INCREASE & DECREASE

11. A number increases from 200 to 240. The percentage increase is:
A) 10%
B) 15%
C) 20%
D) 25%

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12. The price of an item decreases from ₹500 to ₹425. Find the decrease percentage.
A) 10%
B) 12.5%
C) 15%
D) 17.5%

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13. A quantity is increased by 10%. The new quantity is 550. Original quantity is:
A) 450
B) 500
C) 520
D) 600

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14. A number is reduced by 20% and becomes 400. The original number is:
A) 450
B) 480
C) 500
D) 520

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15. If a number is increased by 25%, it becomes 250. The number is:
A) 180
B) 200
C) 225
D) 240

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🔹 LEVEL 4: SUCCESSIVE PERCENTAGES

16. A value is increased by 10% and then by 20%. The net increase is:
A) 30%
B) 32%
C) 28%
D) 25%

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17. If a price is reduced by 10% and then by another 10%, the total reduction is:
A) 20%
B) 18%
C) 19%
D) 21%

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🔹 LEVEL 5: APPLICATION BASED

18. A student scores 450 out of 600 marks. His percentage is:
A) 70%
B) 72%
C) 75%
D) 80%

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19. The population of a town increases from 20,000 to 22,000. The percentage increase is:
A) 8%
B) 9%
C) 10%
D) 12%

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20. If the price of sugar is ₹45 per kg, what is the price after a 20% increase?
A) ₹50
B) ₹52
C) ₹54
D) ₹56

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🔹 LEVEL 6: DISCOUNT & PROFIT IDEA

21. A shirt marked ₹1000 is sold at 20% discount. Selling price is:
A) ₹750
B) ₹780
C) ₹800
D) ₹850

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22. An item is sold for ₹540 after giving 10% discount. The marked price is:
A) ₹600
B) ₹580
C) ₹620
D) ₹650

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23. If cost price is ₹800 and profit is 25%, selling price is:
A) ₹950
B) ₹1000
C) ₹1050
D) ₹1100

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🔹 LEVEL 7: TRICKY MCQs

24. 50% of 60% of a number is 120. The number is:
A) 300
B) 400
C) 500
D) 600

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25. Which of the following is maximum?
A) 40%
B) 2/5
C) 0.38
D) 0.4

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26. If 15% of x = 20% of y, then x : y = ?
A) 3 : 4
B) 4 : 3
C) 2 : 5
D) 5 : 2

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27. A number is first increased by 20% and then decreased by 20%. Net result is:
A) No change
B) 4% increase
C) 4% decrease
D) 2% decrease

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28. 35% of a number is equal to 70. The number is:
A) 180
B) 200
C) 220
D) 250

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29. What percent of 250 is 75?
A) 25%
B) 30%
C) 35%
D) 40%

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30. 12.5% is equal to:
A) 1/4
B) 1/6
C) 1/8
D) 1/10

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✅ ANSWER KEY

1️⃣ C
2️⃣ C
3️⃣ C
4️⃣ B
5️⃣ A
6️⃣ C
7️⃣ C
8️⃣ A
9️⃣ A
🔟 C
1️⃣1️⃣ C
1️⃣2️⃣ B
1️⃣3️⃣ B
1️⃣4️⃣ C
1️⃣5️⃣ B
1️⃣6️⃣ B
1️⃣7️⃣ B
1️⃣8️⃣ C
1️⃣9️⃣ C
2️⃣0️⃣ C
2️⃣1️⃣ C
2️⃣2️⃣ A
2️⃣3️⃣ B
2️⃣4️⃣ B
2️⃣5️⃣ D
2️⃣6️⃣ B
2️⃣7️⃣ C
2️⃣8️⃣ B
2️⃣9️⃣ B
3️⃣0️⃣ C