The circumference of a circular track is 9km. A cyclist rides round it a number of times and stops after…

Analyze the question

The track is a circle with circumference 9 km. Every 9 km the cyclist completes one full lap and is back at the start. So we only need the leftover distance after removing all complete laps.

Concept

Distance from the start (measured along the track) = remainder when 302 is divided by 9.

Solution

302 ÷ 9:

• 9 × 33 = 297
• 302 − 297 = 5

So the cyclist completes 33 full laps and then rides 5 km more.

Check with the digit-sum trick: 3 + 0 + 2 = 5, and 5 is less than 9, so the remainder is 5. ✔

Interpreting "how far from the starting point"

The cyclist is 5 km along the track from the start. This is the distance travelled along the track, which is what the options reflect. (Strictly, the straight-line distance would be a chord, but that would need the track's radius and would not be a whole number like the options, so the question intends the distance along the track.)

Also note that 5 km is more than half of the 9 km circumference (4.5 km). Going the other way round the track, the cyclist would be 4 km from the start. But 4 km is not among the options, and 5 km is the distance along the direction of travel, so the intended answer is 5 km.

Answer: A. 5 km

Exam tip: For "going round a circular track" questions, always divide the total distance by the circumference and use the remainder. You can quickly find remainders when dividing by 9 by adding the digits of the number.