Question

There is a circular path around a circular garden. What is the width of the path?
I) The radius of the circular garden is 20 meters.
II) The circumference of the circular garden is 125 meters and the radius of the circular path around it is 25 meters.

• A. Statement I alone is sufficient to answer the question
• B. Statement II alone is sufficient to answer the question.
• C. Statement I and II together are sufficient to answer the question but neither statement alone is sufficient.
• D. Statement I and II together are not sufficient to answer the question and additional data is required.

Hint:

For circular path problems, always find inner and outer radii. Width is simply their difference.

Answer 1

The Correct Option is B

Concept: Width of the circular path = Outer radius $-$ Inner radius.
Step 1: Analyze Statement I alone.
Radius of garden = 20 m.
Outer radius (path boundary) is unknown.
Statement I alone is NOT sufficient.
Step 2: Analyze Statement II alone.
Circumference of garden = 125 m: \[ 2\pi r = 125 \Rightarrow r \approx 20 { m} \] Outer radius = 25 m.
\[ {Width} = 25 - 20 = 5 { m} \] A unique value is obtained.
Statement II alone is sufficient.
Step 3: Combine both statements.
Not required, since Statement II alone is sufficient.
Hence, Statement II alone is sufficient.