A car runs 10,000 miles using 5 tyres interchangeably. To have equal wear on…

Concept: When a car uses a fixed number of tyres at any moment but rotates among a larger set so every tyre wears out equally, the total wear (in tyre-miles) equals the distance travelled multiplied by the number of tyres in use at once; sharing that total equally across all available tyres gives the mileage each individual tyre runs.

1. A car has 4 tyres bearing its weight at any instant, so travelling 10,000 miles produces a total wear of 10,000 × 4 = 40,000 tyre-miles.

2. The 5 tyres are rotated interchangeably so that this total wear is shared equally among all of them.

3. Each tyre's share = 40,000 ÷ 5 = 8,000 miles.

Cross-check: If each of the 5 tyres runs 8,000 miles, the total wear produced is 5 × 8,000 = 40,000 tyre-miles, which matches 4 × 10,000 — confirming the calculation is consistent.

So, each tyre should have run 8,000 miles.