1. Given data

• Concave mirror radius of curvature: $R = 40\,\text{cm}$
• Hence focal length: $f = \frac{R}{2} = 20\,\text{cm}$

Using Cartesian sign convention for mirrors:

• For a concave mirror, $f = -20\,\text{cm}$
• Object distances are in front of the mirror, so $u_A = -15\,\text{cm}, \qquad u_B = -25\,\text{cm}$

We use mirror formula: $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$

2. Image of object A

For object $A$: $\frac{1}{-20} = \frac{1}{v_A} + \frac{1}{-15}$ $\frac{1}{v_A} = -\frac{1}{20} + \frac{1}{15}$ Taking LCM $60$: $\frac{1}{v_A} = \frac{-3 + 4}{60} = \frac{1}{60}$ So, $v_A = 60\,\text{cm}$

Since $v_A$ is positive, the image is behind the mirror.

3. Image of object B

For object $B$: $\frac{1}{-20} = \frac{1}{v_B} + \frac{1}{-25}$ $\frac{1}{v_B} = -\frac{1}{20} + \frac{1}{25}$ Taking LCM $100$: $\frac{1}{v_B} = \frac{-5 + 4}{100} = -\frac{1}{100}$ Thus, $v_B = -100\,\text{cm}$

Since $v_B$ is negative, the image is in front of the mirror.

4. Distance between the two images

• Image of $A$ is at $+60\,\text{cm}$
• Image of $B$ is at $-100\,\text{cm}$

Distance between them: $|v_A - v_B| = |60 - (-100)| = 160\,\text{cm}$

5. Option check

• A: $60\,\text{cm}$ ❌
• B: $40\,\text{cm}$ ❌
• C: $160\,\text{cm}$ ✅
• D: $100\,\text{cm}$ ❌

Therefore, the correct answer is Option C.