Here on this page Percentages Questions with Answers are provided.  Students can practice these questions based on percentages to prepare for the upcoming exams. You will also get some basic conversion formulas.

### Finding the Percentage of a Number:

• Explain how to calculate a percentage of a given number using the formula: $Percentage = \left ( \frac{Percentage.value}{Total.Value} \right )\times100$
• Provide examples and step-by-step explanations of solving percentage problems.

### Percentage Increase and Decrease:

• Discuss how to determine the percentage increase or decrease between two values using the formula: $Percentage Change= \left ( \frac{Final.value – Initial.value}{Total.Value} \right )\times100$
• Provide practical examples, such as price changes, population growth rates, or test score improvements.

### Applications of Percentages in Real Life:

• Explore various scenarios where percentages are commonly used, such as discounts and sales, interest rates, inflation, and stock market changes.
• Explain the importance of understanding percentages in personal finance and decision making.

### Calculating Percentages in Statistics:

• Discuss the role of percentages in statistics, such as calculating proportions, relative frequencies, and percentages in surveys or data analysis.
• Highlight the significance of percentages in representing data and making meaningful comparisons.

### Solving Percentage Problems:

• Provide a series of practice problems covering different percentage scenarios, including finding percentages, solving for original values, and determining percentage changes.
• Offer step-by-step solutions and explanations to help users understand the problem-solving process.

### Fraction to Percentage Conversion

 $\frac{1}{3}$ × 100 = 33.33% $\frac{1}{10}$ × 100 = 10% $\frac{1}{4}$ × 100 = 25% $\frac{1}{11}$ × 100 = 9.09% $\frac{1}{5}$ × 100 = 20% $\frac{1}{12}$ × 100 = 8.33% $\frac{1}{6}$ × 100 = 16.66% $\frac{1}{13}$ × 100 = 7.69% $\frac{1}{7}$ × 100 = 14.28% $\frac{1}{14}$ × 100 = 7.14% $\frac{1}{8}$ × 100 = 12.5% $\frac{1}{15}$ × 100 = 6.66% $\frac{1}{9}$ × 100 = 11.11% $\frac{1}{16}$ × 100 = 6.25%

### Few Examples on Percentages :

Question 1. Luaa spends her monthly salary in the following manner: 20% on house rent, 20% on food, 5 % on transportation, 10% on the education, and 20% on other household expenses. She saves the remaining amount of ₨. 5000 at the end of the month. Find out her monthly salary?

Options:

A. Rs. 35000

B. Rs. 25000

C. Rs. 20000

D. Rs. 30000

Solution:     Let the

Monthly Salary = 100%

Monthly Expenditure =

20% + 20% + 5% + 10% + 20% = 75%

Monthly Savings = 100% – 75% = 25%

Now, 25% of salary saved = 5000

Let’s take 100% salary as x

25% of x = 5000

x = 5000  × $\frac{100}{25}$

x = $\frac{500000}{25}$

x = 20000

Therefore, her monthly salary = Rs. 20000

Correct option: C

Question 2.Aman spends 60% of his income. Suppose his income is increased by 21% and his expenditure increases by 5%, then what is the increase in his savings (in percentage)?

Options:

A. 60%

B. 18%

C. 40%

D. 45%

Solution:     Let Aman’s income = 100

Expenditure = 60 and

Savings = 40 (We get 40 by subtracting, 100 – 60)

New Income is increased by 21% = 100 + 21 = 121

Expenditure Increased by 5% = 5% more than 60 = 105% of 60 = 63

New Savings = 121 – 63 = 58

Therefore, increase in savings = 58 – 40 = 18

Increase in % = $\frac{18}{40}$ × 100 = 45%

Correct option: D

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## Practice Questions based on Percentages

1. A man made a contribution of 7% of his income to a needy person and saved 25% of the balance. If he now has, Rs. 2100 left, then find his actual income?

9626.26

9626.26

16.96%

9727.27

9727.27

15.31%

3010.75

3010.75

61.53%

10000

10000

6.2%

Let's assume the man's actual income is "X" rupees.

Step 1: Contribution to the needy person Amount contributed = 7% of X = 0.07X

Remaining balance = X - 0.07X = 0.93X

Step 2: Savings from the remaining balance Amount saved = 25% of (0.93X) = 0.25 * 0.93X = 0.2325X

Remaining balance after savings = 0.93X - 0.2325X = 0.6975X

Step 3: The remaining balance is given as Rs. 2100 0.6975X = 2100

Now, solve for X: X = 2100 / 0.6975 ≈ 3010.75

So, the correct value for the man's actual income is indeed Rs. 3010.75.

2. If Jenny’s income is 30% more than that of Nikita, how much percent of Nikita’s income is less than that of Jenny?

23.08%

23.08%

72.32%

25.5%

25.5%

8.1%

27.60%

27.60%

6.36%

29%

29%

13.21%

Let Nikita’s income be 100

Then, Jenny’s income = 130

If Jenny’s income is 130, Nikita’s income = 100

If Jenny’s income is 100, Nikita’s income = 100/130 *100 = 76.92

Therefore, Nikita’s income is less than Jenny’s income by 100 – 76.92 = 23.08%

3. In an examination, 40% are passing percentage. If a person gets 41 marks and fails by 3 marks, what are the maximum marks?

110

110

84.14%

100

100

7.93%

120

120

5.71%

150

150

2.22%

Total passing marks = 41 + 3 = 44

Let maximum marks be m

Then, 40% of m = 44

= 40m/100 = 44

40m = 4400

m = 110

4. If the price of an article is increased by 18%, determine by how much percent must a user reduce the use, so that expenditure on it remains unchanged?

13.24%

13.24%

12.71%

16%

16%

14.16%

25%

25%

6.66%

15.3%

15.3%

66.46%

Decrease in consumption

=$\frac{18}{(100 +18)} \times 100$

= 15.3%

5. Reema saves 51% of his total income of Rs. 15000 per month. Calculate his total spending.

7350

7350

82.07%

7550

7550

11.12%

6500

6500

3.56%

8560

8560

3.24%

Money spent = (100 – 51) of 15000

= 49% of 15000

= 49/100*15000 = 7350

6. If a girl’s height is 15% less than a boy, how much percent of Boy’s height is more than a girl?

22%

22%

4.56%

12.5%

12.5%

16.69%

17.64%

17.64%

72.99%

22.8%

22.8%

5.76%

Excess of boy’s height over girl = 15/ (100-15) *100

= 15/85*100

= 17.64%

7. If 60% of the number is added by 100, then the number becomes the initial number only. Find the number.

350

350

4.59%

280

280

8.65%

200

200

7.99%

250

250

78.77%

Let the number be z

Given, 60% of z + 100 = z

60/100 * z + 100 = z

60z + 10000 = 100z

40z = 10000

z = 250

8. Smith gets a commission of 2% of total sales. He also gets a bonus of 1% if the sale exceeds Rs. 85000. If he received a total commission of Rs. 2500, then calculate how much bonus he received?

266.66

266.66

59.34%

205.55

205.55

21.58%

310

310

9.96%

212.12

212.12

9.13%

Commission up to 85000 = 85000 * 2/100 = 1700

Again after 85000,

Commission: Bonus = 2 : 1 = 2x : x

Therefore, bonus = (2500-1700) * 1/3 = 800*1/3 = Rs. 266.66

9. What percent of 12Kg is 500grams?

5.2%

5.2%

8.56%

4.1%

4.1%

77.33%

1.2%

1.2%

6.17%

4.3%

4.3%

7.93%

1 Kg = 1000grams

12kg = 12000 grams

Percentage = 500/12000 * 100 = 4.16%

10. Express the ratio 8: 5 in percentage.

112%

112%

4.77%

160%

160%

87.04%

114%

114%

3%

180%

180%

5.18%

8 : 5 = 8/5

Percentage = 8/5 * 100 = 160%

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