Percentage Questions with Solutions

Question 1: If 25% of a number is 30, what is the number?

Solution:

Let the number be ‘x’.
25% of x = 30
(25/100) × x = 30
x = (30 × 100) / 25
x = 120

Question 2: A store increased the price of a product by 15%. If the original price was $80, what is the new price?

Solution:

Original price = $80
Increase = 15% of $80 = (15/100) × $80 = $12
New price = Original price + Increase = $80 + $12 = $92

Question 3: A student scored 75% in a test. If the total marks in the test were 200, how many marks did the student score?

Solution:

Percentage score = 75%
Total marks = 200
Marks scored = (75/100) × 200 = 150

Question 4: A discount of 20% is applied to a $250 item. What is the discounted price?

Solution:

Original price = $250
Discount = 20% of $250 = (20/100) × $250 = $50
Discounted price = Original price – Discount = $250 – $50 = $200

Question 5: If 40% of a number is 120, what is 10% of the same number?

Solution:

Let the number be ‘x’.
40% of x = 120
(40/100) × x = 120
x = (120 × 100) / 40
x = 300
10% of the same number = 10% of 300 = (10/100) × 300 = 30

Question 6: If 15% of a number is 45, what is 30% of the same number?

Solution:

Let the number be ‘x’.
15% of x = 45
(15/100) × x = 45
x = (45 × 100) / 15
x = 300
30% of the same number = 30% of 300 = (30/100) × 300 = 90

Question 7: A store reduced the price of a product by 25%. If the original price was $200, what is the discounted price?

Solution:

Original price = $200
Reduction = 25% of $200 = (25/100) × $200 = $50
Discounted price = Original price – Reduction = $200 – $50 = $150

Question 8: A student scored 80% in a test. If the total marks in the test were 150, how many marks did the student score?

Solution:

Percentage score = 80%
Total marks = 150
Marks scored = (80/100) × 150 = 120

Question 9: A discount of 15% is applied to a $180 item. What is the discounted price?

Solution:

Original price = $180
Discount = 15% of $180 = (15/100) × $180 = $27
Discounted price = Original price – Discount = $180 – $27 = $153

Question 10: If 30% of a number is 90, what is 20% of the same number?

Solution:

Let the number be ‘x’.
30% of x = 90
(30/100) × x = 90
x = (90 × 100) / 30
x = 300
20% of the same number = 20% of 300 = (20/100) × 300 = 60

Related Resources:

• Percentage Change
• Percentage Increase
• Percentage Decrease

Question 11: If 18% of a number is 72, what is 45% of the same number?

Solution:

Let the number be ‘x’.
18% of x = 72
(18/100) × x = 72
x = (72 × 100) / 18
x = 400
45% of the same number = 45% of 400 = (45/100) × 400 = 180

Question 12: A store initially increased the price of a product by 20% and then reduced the resulting price by 15%. If the original price was $150, what is the final selling price?

Solution:

Original price = $150
Increase = 20% of $150 = (20/100) × $150 = $30
Price after the increase = Original price + Increase = $150 + $30 = $180
Reduction = 15% of $180 = (15/100) × $180 = $27
Final selling price = Price after the increase – Reduction = $180 – $27 = $153

Question 13: A student scored 75% in a test. If the total marks in the test were 250 and the passing marks were 40% of the total marks, did the student pass the test?

Solution:

Percentage score = 75%
Total marks = 250
Passing marks = 40% of 250 = (40/100) × 250 = 100
Since the student scored 75%, which is less than 100, the student did not pass the test.

Question 14: A discount of 25% is applied to an item. If the discounted price is $112.50, what was the original price?

Solution:

Discounted price = $112.50
Discount = Original price – Discounted price
Original price = Discounted price + Discount
Original price = $112.50 + (25% of $112.50) = $112.50 + $28.13 = $140.63

Question 15: If 40% of a number is 64, what is 25% less than that number?

Solution:

Let the number be ‘x’.
40% of x = 64
(40/100) × x = 64
x = (64 × 100) / 40
x = 160
25% less than that number = 75% of x = 75% of 160 = (75/100) × 160 = 120

Question 16: A shopkeeper marked up the price of a product by 60%. During a sale, the shop offered a discount of 20% on the marked price. If the customer paid $180, what was the original marked price?

Solution:

Let the original marked price be ‘x’.
Marked up price = 160% of x = 1.6x
After a 20% discount, the customer paid $180:
80% of marked up price = $180
0.8x = $180
x = $180 / 0.8 = $225
So, the original marked price was $225.

Question 17: A company’s profit decreased by 25% one year and increased by 40% the following year. If the company’s initial profit was $80,000, what is the final profit after two years?

Solution:

Initial profit = $80,000
After a 25% decrease, the profit becomes 75% of the initial profit:
Year 1 profit = 75% of $80,000 = 0.75 × $80,000 = $60,000
In the following year, the profit increased by 40%:
Year 2 profit = 140% of Year 1 profit = 1.4 × $60,000 = $84,000
So, the final profit after two years is $84,000.

Question 18: A car was purchased for $20,000 and its value depreciated by 15% each year. What will be the car’s value after 5 years?

Solution:

Initial value of the car = $20,000
Depreciation rate = 15% per year
After 1 year, the car’s value is 85% of the initial value:
Year 1 value = 85% of $20,000 = 0.85 × $20,000 = $17,000
Similarly, after 2 years, the car’s value is 85% of Year 1 value:
Year 2 value = 85% of $17,000 = 0.85 × $17,000 = $14,450
Continuing this pattern, after 5 years, the car’s value is $11,635.

Question 19: If a laptop is sold for $450 after applying a 10% discount, what was its original price before the discount?

Solution:

Let the original price be ‘x’.
After a 10% discount, the laptop is sold for 90% of the original price:
90% of x = $450
0.9x = $450
x = $450 / 0.9 = $500
So, the original price was $500.

Question 20: A company’s revenue increased by 20% one year and then decreased by 15% the following year. If the company’s initial revenue was $150,000, what is the final revenue after two years?

Solution:

Initial revenue = $150,000
After a 20% increase, the revenue becomes 120% of the initial revenue:
Year 1 revenue = 120% of $150,000 = 1.2 × $150,000 = $180,000
In the following year, the revenue decreased by 15%:
Year 2 revenue = 85% of Year 1 revenue = 0.85 × $180,000 = $153,000
So, the final revenue after two years is $153,000.

Question 21: A software company hired 100 employees, of which 60% are software developers and the rest are testers. If the company wants to increase the number of testers by 40%, how many more testers need to be hired?

Solution:

Number of software developers = 60% of 100 = 0.6 × 100 = 60 employees
Number of testers initially = 100 – 60 = 40 employees
To increase testers by 40%, 40% of the current number of testers need to be hired:
Additional testers needed = 40% of 40 = 0.4 × 40 = 16 testers

Question 22: A stock’s value increased by 25% in the first year and then decreased by 20% in the second year. If the stock’s original value was $200, what is its final value after two years?

Solution:

Original value of the stock = $200
After a 25% increase in the first year, the value becomes 125% of the original value:
Year 1 value = 125% of $200 = 1.25 × $200 = $250
In the second year, the value decreased by 20%, which is 80% of Year 1 value:
Year 2 value = 80% of $250 = 0.8 × $250 = $200
So, the final value after two years is $200.

Question 23: A company’s profit decreased by 10% one year and increased by 15% the following year. If the company’s initial profit was $120,000, what is the final profit after two years?

Solution:

Initial profit = $120,000
After a 10% decrease, the profit becomes 90% of the initial profit:
Year 1 profit = 90% of $120,000 = 0.9 × $120,000 = $108,000
In the following year, the profit increased by 15%:
Year 2 profit = 115% of Year 1 profit = 1.15 × $108,000 = $124,200
So, the final profit after two years is $124,200.

Question 24: A laptop is sold for $800 after applying a 20% profit margin. What was the cost price of the laptop before the profit was added?

Solution:

Let the cost price be ‘x’.
After a 20% profit, the selling price becomes 120% of the cost price:
120% of x = $800
1.2x = $800
x = $800 / 1.2 = $666.67 (rounded to two decimal places)
So, the cost price of the laptop before the profit was added was approximately $666.67.

Question 25: A company’s revenue increased by 15% one year and then decreased by 10% the following year. If the company’s initial revenue was $250,000, what is the final revenue after two years?

Solution:

Initial revenue = $250,000
After a 15% increase, the revenue becomes 115% of the initial revenue:
Year 1 revenue = 115% of $250,000 = 1.15 × $250,000 = $287,500
In the following year, the revenue decreased by 10%, which is 90% of Year 1 revenue:
Year 2 revenue = 90% of $287,500 = 0.9 × $287,500 = $258,750
So, the final revenue after two years is $258,750.

Percentage calculations are a basic but crucial part of math. Whether you’re a student getting ready for exams or just want to improve your math skills, understanding percentages is important. In this collection of percentage questions, we’ve made it easy for you to practice and learn this essential math concept.

Our team of experts has created these questions to align with the latest exam formats and follow the NCERT curriculum and CBSE syllabus for 2023-2024. Each question is designed to help you become more confident in dealing with percentages and solving related problems.

Join us as we explore the world of percentages and provide you with a user-friendly way to master this important aspect of math.

Some Formulas for Percentages

1. Percentage Calculation:
   • Percentage = (Part / Whole) × 100%
2. Percentage Change:
   • Percentage Change = ((New Value – Old Value) / Old Value) × 100%
3. Percentage of a Number:
   • Percentage of a Number = (Percentage / 100) × Number
4. Percentage Profit and Loss:
   • Percentage Profit = ((Selling Price – Cost Price) / Cost Price) × 100%
   • Percentage Loss = ((Cost Price – Selling Price) / Cost Price) × 100%
5. Discount Percentage:
   • Discount Percentage = (Discount / Marked Price) × 100%
6. Simple Interest:
   • Simple Interest = (Principal × Rate × Time) / 100
7. Compound Interest:
   • Compound Interest =