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Maths Olympiad Questions for Class 8 with Answers

“I knew the chapter, but I had no idea how to begin.” Many class 8 students say this after their first olympiad paper, and it’s a fair complaint. The topics are the ones you study in school. The questions just come at them from an odd angle. Practising maths olympiad questions for class 8 teaches you to spot that angle.

This page has 20 solved questions and five more for you to try alone. Cover the answer, give each question a real attempt, and only then read on. Getting stuck for a few minutes is part of the process.

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Maths Olympiad questions for Class 8 students to practice problem-solving and mathematical reasoning.
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    What Is a Maths Olympiad?

    It’s a competitive exam that rewards clear thinking over memory. In India, class 8 students usually write the International Mathematics Olympiad (IMO), conducted by the Science Olympiad Foundation (SOF). Plenty of schools also run their own olympiad-style tests.

    Is it worth the effort? Yes, for a few reasons. Your basics get stronger, so school exams start to feel lighter. You learn to work quickly without panicking. And it gives you a head start for classes 9 and 10, where the questions get tougher. Some students also simply enjoy it, because olympiad problems feel more like puzzles than homework.

    What to Study

    There’s no separate syllabus. Questions come from the chapters you already know: rational numbers, linear equations, quadrilaterals, data handling and probability, squares and cubes, comparing quantities, algebraic identities and factorisation, exponents, proportion and mensuration.

    Papers also carry logical reasoning, everyday mathematics and a harder achievers section. The pattern changes now and then, so check the official website for the latest format before you plan your revision.

    Maths Olympiad Questions for Class 8 with Answers

    Think of this set as a starter pack of math olympiad problems for grade 8. It runs chapter by chapter, and I’ve added a note wherever students commonly slip.

    Rational Numbers

    Q1. Find a rational number between 1/3 and 1/2.

    The quickest way is to take the average. (1/3 + 1/2) ÷ 2 = 5/12. Since 0.33 < 0.42 < 0.5, the answer is 5/12.

    Q2. The sum of two rational numbers is 5/6. One of them is −2/3. Find the other.

    Subtract the known number from the sum: 5/6 − (−2/3) = 5/6 + 4/6 = 3/2.

    Linear Equations

    Q3. Solve (x + 2)/3 − (x − 1)/4 = 1.

    Clear the fractions first by multiplying everything by 12:

    4(x + 2) − 3(x − 1) = 12
     4x + 8 − 3x + 3 = 12
     x = 1

    Be careful with the minus sign before the second bracket. It changes both terms inside, and writing −3x − 3 is one of the most common slips on this type of question.

    Q4. A father is three times as old as his son. After 10 years he will be twice as old. Find their present ages.

    Let the son be x, so the father is 3x. In ten years: 3x + 10 = 2(x + 10), which gives x = 10. The son is 10 and the father is 30.

    Q5. The digits of a two-digit number add up to 9. Reversing the digits gives a number 27 more than the original. Find the number.

    Let the digits be t (tens) and u (units), so t + u = 9. The reversed number minus the original is (10u + t) − (10t + u) = 9(u − t), and that equals 27, so u − t = 3. Now you have two simple equations: u = 6 and t = 3. The number is 36, and 63 − 36 = 27 confirms it.

    Quadrilaterals

    Q6. The angles of a quadrilateral are in the ratio 2 : 3 : 4 : 6. Find the largest.

    The angles add up to 360° and the ratio has 15 parts, so one part is 24°. The largest angle is 6 × 24° = 144°.

    Q7. Each exterior angle of a regular polygon is 40°. How many sides does it have, and what is each interior angle?

    Exterior angles always total 360°, so there are 360 ÷ 40 = 9 sides. Each interior angle is 180° − 40° = 140°.

    Probability

    Q8. A die is rolled once. What is the probability of getting a prime number?

    The primes on a die are 2, 3 and 5, so that’s 3 out of 6, or 1/2. Notice that 1 is not prime. Students forget this more than you’d expect.

    Squares, Cubes and Roots

    Q9. Find the smallest number by which 1620 should be multiplied to get a perfect square.

    Write 1620 = 2² × 3⁴ × 5. Every prime appears in a pair except 5, so multiply by 5. You get 8100, which is 90².

    Q10. Find the square root of 7056 using prime factorisation.

    7056 = 2⁴ × 3² × 7². Take one from each pair: 2² × 3 × 7 = 84.

    Q11. How many natural numbers lie between 30² and 31²?

    Between n² and (n + 1)² there are 2n numbers. Here that’s 60. It’s worth remembering as a shortcut, because it comes up often.

    Q12. By what smallest number should 1372 be divided to make it a perfect cube?

    1372 = 2² × 7³. The 7³ is already a cube, but the 2² is not, so divide by 2² = 4. That leaves 343, which is 7³.

    Comparing Quantities

    Q13. A shopkeeper marks an article 25% above cost and then gives a 10% discount. Find his profit percent.

    Assume the cost price is ₹100. The marked price is ₹125, and after a 10% discount (₹12.50 off) the selling price is ₹112.50. Profit = 12.5%. The discount applies to the marked price, not the cost price. That’s the whole trick.

    Q14. Find the compound interest on ₹10,000 for 2 years at 10% per annum, compounded annually.

    Amount = 10,000 × 1.1 × 1.1 = ₹12,100. Interest = 12,100 − 10,000 = ₹2,100.

    Algebra

    Q15. If a + b = 10 and ab = 21, find a² + b².

    You don’t need to find a and b at all. Use a² + b² = (a + b)² − 2ab = 100 − 42 = 58.

    Q16. Factorise x² − 5x − 24.

    Look for two numbers that multiply to −24 and add to −5: they are −8 and 3. So x² − 8x + 3x − 24 = x(x − 8) + 3(x − 8) = (x − 8)(x + 3).

    Exponents

    Q17. Simplify (3⁻¹ + 4⁻¹)⁻¹.

    Add inside the bracket first: 1/3 + 1/4 = 7/12. Then take the reciprocal to get 12/7. Flipping each term separately is the usual wrong turn here.

    Proportion

    Q18. 12 workers finish a job in 15 days. How long will 20 workers take?

    More workers means fewer days, so it’s an inverse proportion. 12 × 15 = 20 × d, which gives d = 9 days.

    Mensuration

    Q19. The total surface area of a cube is 384 cm². Find its volume.

    A cube has 6 faces, so 6a² = 384. That gives a² = 64 and a = 8 cm. Volume = 8³ = 512 cm³.

    Q20. A cylinder has radius 7 cm and height 10 cm. Find its curved surface area and volume. (Take π = 22/7.)

    Curved surface area = 2πrh = 2 × 22/7 × 7 × 10 = 440 cm².
     Volume = πr²h = 22/7 × 49 × 10 = 1540 cm³.

    Try These Yourself

    These work well as practice problems for class 8 math competitions. The answers are given, so you can check yourself once you’re done.

    1. The sum of three consecutive multiples of 5 is 105. Find them. (30, 35, 40)
    2. Find the smallest square number divisible by 6, 8 and 12. (144)
    3. A rectangle’s length is 5 cm more than its breadth, and its perimeter is 50 cm. Find its area. (150 cm²)
    4. Factorise 4x² − 25y². ((2x − 5y)(2x + 5y))
    5. A town of 20,000 people grows 10% every year. What is its population after 2 years? (24,200)

    Where to Find More Practice

    Once these start to feel comfortable, look for 8th grade maths olympiad practice questions in workbooks that show full solutions. A solution you can follow is worth more than a bare answer key. Class 8 competitive maths questions from talent-search style tests are also useful, because they train the same logic and number sense. And don’t ignore your own school tests. Try the hardest question on each one first.

    Try a Sample Paper With a Timer

    Sooner or later, sit down with a sample maths olympiad paper for class 8 and a clock. You’ll see how the real paper feels and where your time goes. The SOF website usually lists sample papers, though what’s available changes, so check the current page. Your maths teacher may have old papers, and many workbooks include model papers with answer keys. Stick to trusted sources, because a wrong answer key can teach you a wrong method.

    How to Prepare

    Start with your NCERT basics, since olympiad questions grow out of the same ideas. Spend five to ten minutes on a problem before you look at the solution. Keep a small notebook for formulas and for mistakes you repeat. Work chapter by chapter first, then move to timed papers. A few days later, redo the questions you got wrong. If you can solve them without help, you’ve really learned them. It also saves time to know your squares up to 30 and cubes up to 10 by heart.

    On the Day of the Exam

    Begin with questions that feel easy and return to the harder ones later. If a problem eats up four or five minutes, leave it and come back. In multiple-choice questions, cross out the options you know are wrong before guessing. And before you move on, glance at signs, units and what the question actually asked for.

    Conclusion

    Solve a few problems each day, look closely at the ones you get wrong, and build up slowly to full timed papers. Give it a few weeks. Maths olympiad questions for class 8 will stop feeling scary, and your school maths will likely feel easier too.

    Frequently Asked Questions

    Usually, yes. The syllabus overlaps, but olympiad questions make you use ideas in unfamiliar ways.

    Thirty to sixty minutes of focused work, along with regular school study, is enough for most students.

    It’s the foundation. Add a good workbook and sample papers on top.

    Yes. Official sample papers, workbooks and teacher-made worksheets often include answers. Study the method, not just the final number.

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