A can go round a circular path 8 times in 40 minutes. If the diameter of the circle is increased to 10 times the original diameter, then the time required by A to go round the new path once, travelling at the same speed as before, is

### Concept & Distance, Speed, and Time The distance around a circular path is its circumference, which is given by $\pi \times \text{diameter}$ ($\pi d$). Time required is proportional to the distance traveled if the speed remains constant: $$T = \frac{D}{S}$$ ### Step-by-Step Solution * **Given:** 8 rounds take 40 minutes. * **Deduction:** 1 round of the original path takes $\frac{40}{8} = 5$ minutes. * **Calculation:** The original distance for 1 round is $\pi d$. * **Calculation:** The new diameter is $10d$, so the new distance for 1 round is $\pi(10d) = 10(\pi d)$. * **Deduction:** The new path is 10 times as long as the original path. * **Calculation:** Since speed is constant, the time required will also be 10 times the original time. $10 \times 5\text{ minutes} = 50\text{ minutes}$. ### Exam Strategy & Shortcut Realize that distance is directly proportional to diameter. If diameter becomes $10\times$, distance becomes $10\times$. Time for 1 old round is $5\text{ min}$. Therefore, time for 1 new round is $10 \times 5 = 50\text{ min}$. ### Common Pitfall A common error is confusing the number of rounds (8) and applying the multiplier to the total 40 minutes directly without finding the time for a single round first. ### Final Answer Therefore, the correct answer is **50 min.**