Standing on the platform, Amit told Sunita that Aligarh was more that 10 km but less than 15 km from there. Sunita knew that it was more than 12 km but less than 14 km from there. If both of them were correct, which of the following could be the distance of Aligarh from the platform?

Options

A. 11 km
B. 12 km
C. 13 km
D. 14 km

Explanation

To solve the problem, we need to analyze the distance range provided by both Amit and Sunita and find a common distance that satisfies both their statements.

### Step-by-Step Solution:

1. **Understanding Amit's Statement:**
- Amit says that Aligarh is more than 10 km but less than 15 km.
- This can be expressed as:
\[ 10 < \text{Distance} < 15 \]

2. **Understanding Sunita's Statement:**
- Sunita states that Aligarh is more than 12 km but less than 14 km.
- This can be expressed as:
\[ 12 < \text{Distance} < 14 \]

3. **Finding the Overlapping Range:**
- Now, we need to find the overlap between Amit's and Sunita's ranges.
- Amit's range is (10, 15) and Sunita's range is (12, 14).
- The overlapping range can be found by taking the maximum of the lower bounds and the minimum of the upper bounds:
- Lower bound: max(10, 12) = 12
- Upper bound: min(15, 14) = 14
- Therefore, the overlapping range is:
\[ 12 < \text{Distance} < 14 \]

4. **Identifying Possible Distances:**
- The distances that fall within the range of (12, 14) are:
- 13 km (since it is greater than 12 and less than 14)

5. **Conclusion:**
- The only distance that satisfies both Amit's and Sunita's statements is 13 km.

### Final Answer:
The distance of Aligarh from the platform could be **13 km**.