Question

Standing near a bus stop, Ayush told Smitha that Koti was more than ten kilometres but less than 15 kilometres from there. Smitha know that it was more than 12 kilometres but less than fourteen kilometres from there. If both of them were correct, which of the following could be the distance to Koti from the bus stop?

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

Answer 1

The Correct Option is C

This is a logical reasoning problem that requires evaluating the possible distance to Koti from the bus stop based on the statements given by Ayush and Smitha. 

1. Ayush states that the distance to Koti is more than 10 kilometres but less than 15 kilometres. This gives us the range: \(10 \text{ km} < \text{Distance to Koti} < 15 \text{ km}\).
2. Smitha confirms that the distance is more than 12 kilometres but less than 14 kilometres. This gives us another range: \(12 \text{ km} < \text{Distance to Koti} < 14 \text{ km}\).
3. To find the common range where both their statements intersect, we compare the two conditions:
   • From Ayush: \(10 \text{ km} < \text{Distance to Koti} < 15 \text{ km}\)
   • From Smitha: \(12 \text{ km} < \text{Distance to Koti} < 14 \text{ km}\)
   • The overlapping portion of these two ranges is: \(12 \text{ km} < \text{Distance to Koti} < 14 \text{ km}\).
4. Thus, the distance to Koti that satisfies both Ayush and Smitha's statements is between 12 km and 14 km exclusively. The only option that matches this criterion is 13 km.

Therefore, the correct answer is 13 km.