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About Comparing Quantities — Class 8 CBSE

Calculate percentages, profit, loss, discount, tax, and compound interest. This topic is part of the CBSE Class 8 mathematics syllabus (chapter: Chapter 8). On this page you can practice 62 questions across three difficulty levels — 20 easy, 22 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 37-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

Comparing Quantities — solved examples for Class 8 CBSE

Example 1easy

A shopkeeper first increases the price of an item by 20% and then decreases the new price by 20%. Which of the following statements is true about the final price compared to the original price?
  1. A)The final price is the same as the original price.
  2. B)The final price is less than the original price.
  3. C)The final price is more than the original price.
  4. D)The final price depends on the original price value.

Step-by-step solution

  1. Let the original price be ₹100.
  2. Increasing by 20%: New price = 100 + (20/100) × 100 = 100 + 20 = ₹120.
  3. Decreasing the new price by 20%: Decrease amount = (20/100) × 120 = ₹24.
  4. Final price = 120 - 24 = ₹96. Since ₹96 < ₹100, the final price is less than the original price.

Answer: The final price is less than the original price.

Example 2medium

A shirt's price increased by 15% and is now ₹690. What was its original price?
  1. A)₹600
  2. B)₹580
  3. C)₹780
  4. D)₹720

Step-by-step solution

  1. Let the original price be P.
  2. New price = Original price + 15% of Original price = P + 0.15P = 1.15P.
  3. Given new price = ₹690, so 1.15P = 690.
  4. P = 690 / 1.15 = ₹600.

Answer: ₹600

Example 3hard

A shopkeeper first increases the price of an article by 20% and then offers a discount of 10% on the new price. If the final selling price of the article is ₹540, what was the original price of the article?
  1. A)₹500
  2. B)₹480
  3. C)₹520
  4. D)₹600

Step-by-step solution

  1. Let the original price be P.
  2. Price after 20% increase: P × (1 + 20/100) = P × 1.20.
  3. Price after 10% discount on the new price: (1.20P) × (1 - 10/100) = 1.20P × 0.90 = 1.08P.
  4. Given final selling price is ₹540, so 1.08P = 540. Therefore, P = 540 / 1.08 = ₹500.

Answer: ₹500

Practice questions on Comparing Quantities

  1. Q1.easy

    A vendor sells a bicycle. Which of the following conditions must be true for the vendor to make a profit?
    1. A)Selling Price (SP) < Cost Price (CP)
    2. B)Selling Price (SP) = Cost Price (CP)
    3. C)Selling Price (SP) > Cost Price (CP)
    4. D)The item is sold quickly.
    Show answer

    Answer: Selling Price (SP) > Cost Price (CP)

    Hint: Profit occurs when you sell an item for more than what you paid for it.

  2. Q2.easy

    In a school, 40% of the students are girls. If the total number of girls is 240, what is the total number of students in the school?
    1. A)500
    2. B)550
    3. C)650
    4. D)600
    Show answer

    Answer: 600

    Hint: If 40% of the total represents 240 students, you can set up an equation to find the total.

  3. Q3.easy

    Rahul bought a book for ₹200 and sold it for ₹240. He calculated his profit percentage as (₹40 / ₹240) × 100%. Which of the following statements correctly identifies Rahul's mistake?
    1. A)The profit amount is incorrect.
    2. B)The selling price should not be used in the denominator.
    3. C)The calculation should be (₹40 / ₹200) × 100%.
    4. D)Both B and C are correct.
    Show answer

    Answer: Both B and C are correct.

    Hint: Profit percentage is always calculated on the Cost Price (CP), not the Selling Price (SP).

  4. Q4.medium

    In an exam, 80% of the students passed. If there were 2000 students in total, how many students failed?
    1. A)300
    2. B)500
    3. C)400
    4. D)600
    Show answer

    Answer: 400

    Hint: First, find the percentage of students who failed, then calculate that percentage of the total number of students.

  5. Q5.medium

    A shopkeeper bought an article for ₹800. He spent ₹50 on its transportation. He then sold it for ₹1000. Find his profit percentage (rounded to two decimal places).
    1. A)15.00%
    2. B)17.65%
    3. C)20.00%
    4. D)25.00%
    Show answer

    Answer: 17.65%

    Hint: Remember that the total cost price includes the purchase price plus any additional expenses like transportation.

  6. Q6.medium

    An item was sold for ₹480 after a discount of 25% on its Marked Price. What was the Marked Price of the item?
    1. A)₹640
    2. B)₹600
    3. C)₹580
    4. D)₹560
    Show answer

    Answer: ₹640

    Hint: If there's a 25% discount, the selling price represents 100% - 25% of the Marked Price.

  7. Q7.hard

    A man sells two horses for ₹19,500 each. On one he gains 25% and on the other he loses 25%. What is his overall gain or loss percentage in the entire transaction?
    1. A)6.25% gain
    2. B)6.25% loss
    3. C)No gain, no loss
    4. D)12.5% loss
    Show answer

    Answer: 6.25% loss

    Hint: When two articles are sold for the same selling price, and one is sold at x% profit and the other at x% loss, there is always a net loss. Calculate the individual cost prices first.

  8. Q8.hard

    A shopkeeper marks his goods at such a price that after allowing a discount of 20%, he still makes a profit of 25%. If the cost price of an article is ₹1600, what is its marked price?
    1. A)₹2000
    2. B)₹2400
    3. C)₹2500
    4. D)₹2800
    Show answer

    Answer: ₹2500

    Hint: First, calculate the selling price using the profit percentage on the cost price. Then, use the selling price and discount percentage to find the marked price.

  9. Q9.hard

    The price of a washing machine, including 18% GST, is ₹16,520. What is the original price of the washing machine before GST was added?
    1. A)₹14000
    2. B)₹14800
    3. C)₹15000
    4. D)₹14500
    Show answer

    Answer: ₹14000

    Hint: The given price is the original price plus the GST amount. If the original price is 'P', then P + 18% of P equals the total price.

These are 9 of the 62 questions available for Comparing Quantities. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.