Arithmetic Challenge Questions
These questions are designed to stretch your arithmetic thinking. Some require several steps; others demand careful reading. Attempt each one before checking the solution.
Challenge 1 – The Long Journey
A cyclist rides at 18 km/h for 2.5 hours, then rests for 30 minutes, then rides at 24 km/h for 1 hour 45 minutes. What is the total distance covered?
Leg 1: 18 × 2.5 = 45 km. Leg 2: 24 × 1.75 = 42 km. Total = 87 km.
Challenge 2 – The Tile Problem
A bathroom floor is 3.6 m × 2.4 m. Square tiles are 30 cm × 30 cm. Tiles cost £0.85 each. What is the total cost?
Floor area = 3.6 × 2.4 = 8.64 m². Tile area = 0.3 × 0.3 = 0.09 m². Number = 8.64 ÷ 0.09 = 96 tiles. Cost = 96 × £0.85 = £81.60.
Challenge 3 – Sequence Problem
The 5th term of an arithmetic sequence is 23 and the 9th term is 43. Find the first term and the sum of the first 20 terms.
Common difference d = (43−23) ÷ (9−5) = 5. First term a = 23 − 4 × 5 = 3. Sum = 20/2 × (2×3 + 19×5) = 10 × (6 + 95) = 1,010.
More Challenges
- A rope is 12.6 m long. Pieces of 0.7 m are cut. How many pieces and what length remains?
- Three workers earn in ratio 3 : 4 : 5. Total wage = £1,200. How much does each earn?
- A car depreciates by 15% per year. If it is worth £18,000 now, what will it be worth in 2 years?
- Find the value of 2³ + 3² + 4¹ − 5⁰.
- Insert +, −, ×, ÷ and brackets into 3 3 3 3 3 to make 100.