1. Given data

• Length of second hand: $r_s = 75\text{ cm} = 0.75\text{ m}$
• Length of minute hand: $r_m = 60\text{ cm} = 0.60\text{ m}$
• Time interval: $30$ minutes
• Take $\pi = 3.14$

We need the extra distance traveled by the tip of the second hand compared to the tip of the minute hand in $30$ minutes.

2. Distance traveled by tip = number of revolutions $\times$ circumference

For a hand of length $r$, one full revolution covers: $2\pi r$

3. Second hand distance in 30 minutes

The second hand completes 1 revolution per minute.

So in $30$ minutes, number of revolutions: $n_s = 30$

Distance traveled: $d_s = 30 \times 2\pi \times 0.75$ $d_s = 30 \times 2 \times 3.14 \times 0.75$ $d_s = 30 \times 4.71$ $d_s = 141.3\text{ m}$

4. Minute hand distance in 30 minutes

The minute hand completes 1 revolution in 60 minutes.

So in $30$ minutes, number of revolutions: $n_m = \frac{30}{60} = \frac{1}{2}$

Distance traveled: $d_m = \frac{1}{2} \times 2\pi \times 0.60$ $d_m = \pi \times 0.60$ $d_m = 3.14 \times 0.60$ $d_m = 1.884\text{ m}$

5. Required extra distance

$x = d_s - d_m$ $x = 141.3 - 1.884$ $x = 139.416\text{ m}$

Nearly, $x \approx 139.4\text{ m}$

6. Option matching

The nearest option is: $\boxed{\text{C: } 139.4}$

7. Comparison with stored answer

Stored correct answer: C

Our derived answer: C

So, the answer agrees with the stored answer.