Maths Olympiad Questions for Class 5, with Worked Answers
Practise the logic puzzles that set Class 5 olympiad papers apart: heads and legs, coins, ages, handshakes, divisibility and number riddles. Each paper is new, set on Hard, and comes with an OMR sheet and an answer key that shows the working.
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1Class and sections
Class SectionsReasoning: series, odd one out, analogies, coding, directions, mirror images, counting figures, calendar and clock. Maths: patterns, missing numbers, number riddles, logic problems and quick calculation.
2Paper
Number of questions DifficultyEvery click writes a fresh paper with its own answer key, so a class can practise again and again.
3Header and pages
Class 4 · 20 questions · Maths + Reasoning
Practise on screen. Answer this paper on your phone or computer with a countdown, then see the score and the working for each question.
A4 size; print at 100%. The questions are written by this generator in an olympiad style. They are not taken from any past paper, and MuftTools is not connected with any olympiad organiser.
Timed practice
Where Class 5 olympiad maths gets interesting
By Class 5 most children can add, multiply and divide large numbers without trouble. Olympiad-style papers for this class therefore spend fewer marks on plain calculation and more on puzzles that need a plan: two things hidden in one total, a condition that only one number can meet, or a pattern built from two rules. This page opens the generator at Class 5, Maths only, 25 questions on Hard, so these puzzles appear often.
Five puzzle types, with the method
The examples below were written for this page. The generator makes new versions with different numbers on every paper.
Heads and legs
A farm has hens and goats with 15 heads and 40 legs. How many goats? If all 15 were hens there would be 30 legs. The 10 extra legs come from goats, two extra each, so there are 5 goats and 10 hens.
Coins of two kinds
12 coins of ₹2 and ₹5 make ₹39. How many ₹5 coins? Twelve ₹2 coins make ₹24. Each ₹5 coin adds ₹3 more, and ₹15 more is needed, so there are 5 coins of ₹5. Check: 5 × 5 + 7 × 2 = 39.
Ages
Asha is 4 years older than Ravi. In 3 years the sum of their ages will be 30. How old is Ravi now? In 3 years both are 3 years older, so today their ages add to 30 – 6 = 24. Take away Asha's extra 4 and halve: Ravi is 10.
Handshakes and matches
6 friends each shake hands once with every other friend. Each of the 6 shakes 5 hands, but every handshake is counted twice, so 6 × 5 ÷ 2 = 15. The same idea counts matches when every team plays every other team once.
Divisible by both
How many numbers from 1 to 100 are divisible by both 4 and 6? A number divisible by both is divisible by their LCM, 12. The multiples of 12 up to 100 are 12, 24 … 96, which is 8 numbers. A common mistake is to multiply 4 × 6 = 24 and count only 4.
Other questions on the paper
- Number patterns using squares, "multiply then add", and "add the two before".
- Number riddles with two or three clues about digits, such as the sum of the digits or what happens when the digits are swapped.
- Counting questions, such as how many digits are needed to number the pages of a book.
- Missing numbers in longer statements, like 6 × ? – 9 = 39.
- Shapes and measures: perimeter, width from perimeter, and covering a rectangle with unit squares.
Making the most of a hard paper
A Hard paper should feel hard. If a child scores around half on the first try, that is a good starting point. After marking, pick the three wrong answers that look most fixable and redo them with the working line from the key. Then press New questions and try the same level a few days later; the puzzle types repeat with new numbers, so the method sticks.
Many Class 5 olympiad papers also have a reasoning section. Switch Sections to Maths + Reasoning, or see the reasoning questions for Class 5.
More olympiad practice papers
- Class 2 maths olympiad questions
- Class 3 maths olympiad practice paper
- Logical reasoning for Class 4
- Reasoning questions for Class 5
- Reasoning questions for Class 6
- Olympiad OMR sheet
- Free olympiad mock test online
Need more options? Open the full Olympiad Practice Sheets (Maths & Reasoning) with OMR.
Frequently asked questions
Why is this page set to Hard?
Class 5 children who are preparing for an olympiad usually already handle school sums well. The Hard setting brings forward the puzzles that need a method, such as heads and legs or ages, and the harder number patterns. Switch to Medium if the first paper feels too tough.
Can a Class 5 child solve heads-and-legs questions without algebra?
Yes. Assume every animal is a hen, count the legs, and see how many legs are left over. Each goat adds two extra legs, so the leftover legs divided by 2 gives the number of goats. The answer key uses this method.
Are the answers checked?
Every question is built with its answer, and our test suite independently re-solves thousands of generated papers, for example by trying every possible number for a riddle, to make sure exactly one option is right.
Does the paper include geometry?
It includes shapes and measures questions on perimeter and area, and the reasoning section (if you switch it on) adds counting triangles, squares and rectangles in a figure. It does not cover every geometry topic of every olympiad syllabus.
Can my child do it on a phone?
Yes. Press Start timed practice below the preview. The questions open with large tap-friendly options and a countdown, and the score and working appear when your child submits.