In our camp there are 10 soldiers, four of them run at the speed of 7.2 km/hr., 3 at 5.4 km/hr, and another three at 3.6 km/hr. Seeing the liquid missile the soldiers are asked to vacate the camp. Because of the hilly area, the soldiers have to essentially stop for 2 seconds for breathing, after every 30 seconds of run. The missile can kill all life upto exactly 420 m from the camp. Assuming that the missile will exactly hit our camp, answer the following:
Assuming that the missile will exactly hit our camp, answer the following :
How many soldiers will survive if the missile hits 15 seconds late?

Options

A. All 10
B. Four
C. Seven
D. None

Answer

To solve the problem, we need to determine how far each group of soldiers can run in the 15 seconds before the missile hits the camp. We will calculate the distance each group can cover and see if they are within the lethal range of the missile.

### Step-by-Step Solution:

1. **Convert Speeds from km/hr to m/s**:
- For the soldiers running at 7.2 km/hr:
\[ \text{Speed} = 7.2 \times \frac{5}{18} = 2 \text{ m/s} \]
- For the soldiers running at 5.4 km/hr:
\[ \text{Speed} = 5.4 \times \frac{5}{18} = 1.5 \text{ m/s} \]
- For the soldiers running at 3.6 km/hr:
\[ \text{Speed} = 3.6 \times \frac{5}{18} = 1 \text{ m/s} \]

2. **Calculate Distance Covered in 15 Seconds**:
- For the 4 soldiers running at 7.2 km/hr (2 m/s):
\[ \text{Distance} = \text{Speed} \times \text{Time} = 2 \text{ m/s} \times 15 \text{ s} = 30 \text{ m} \]
- For the 3 soldiers running at 5.4 km/hr (1.5 m/s):
\[ \text{Distance} = 1.5 \text{ m/s} \times 15 \text{ s} = 22.5 \text{ m} \]
- For the 3 soldiers running at 3.6 km/hr (1 m/s):
\[ \text{Distance} = 1 \text{ m/s} \times 15 \text{ s} = 15 \text{ m} \]

3. **Determine Total Distance from Camp**:
- The missile can kill all life up to 420 m from the camp. We need to check if any soldier can escape this range.
- The distances from the camp are:
- Soldiers at 7.2 km/hr: 30 m
- Soldiers at 5.4 km/hr: 22.5 m
- Soldiers at 3.6 km/hr: 15 m

4. **Check if Soldiers are within the Lethal Range**:
- All calculated distances (30 m, 22.5 m, and 15 m) are less than 420 m.
- Therefore, all soldiers are still within the lethal range of the missile.

5. **Conclusion**:
- Since all soldiers are within the lethal range of the missile, none of them will survive when the missile hits.

### Final Answer:
**None of the soldiers will survive.**