Question

Rajneetha walks around the circular park in 15 minutes. If she walks at the rate of 5 km/hr, how much distance would she have to travel, at the minimum, to reach the centre of the park from any point on its perimeter?

• A. 100 metre
• B. 200 metre
• C. 250 metre
• D. 300 metre

Hint:

When given walking speed and time around a circle, find circumference, then use \(C = 2\pi r\) to find radius, which gives minimum distance to the centre.

Answer 1

The Correct Option is B

Step 1: Find total distance walked (i.e., circumference)
Speed \( = 5 \text{ km/hr} = 5000 \text{ metres/hr} \)
Time \( = 15 \text{ minutes} = \frac{15}{60} = \frac{1}{4} \text{ hr} \) \[ \text{Distance walked} = \text{Speed} \times \text{Time} = 5000 \times \frac{1}{4} = 1250 \text{ metres} \] So, Circumference of the circular park = 1250 metres Step 2: Use formula for circumference to find radius
\[ C = 2\pi r \Rightarrow 1250 = 2 \times \pi \times r \Rightarrow r = \frac{1250}{2\pi} = \frac{625}{\pi} \] Take \(\pi \approx 3.14\): \[ r = \frac{625}{3.14} \approx 199 \text{ metres} \approx 200 \text{ metres} \] Radius of the circular park \( \approx 200 \text{ metres} \) Step 3: Minimum distance from perimeter to centre = radius
Therefore, minimum distance to reach centre \(= \boxed{200 \text{ metres}} \)