Question:
What is the distance between two cities A and B?
Statement (I): A cyclist takes one hour more to reach B from A than reaching A from B.
Statement (II): The speed of the cyclist is 10 kmph.
What is the distance between two cities A and B?
Statement (I): A cyclist takes one hour more to reach B from A than reaching A from B.
Statement (II): The speed of the cyclist is 10 kmph.
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To determine a unique distance, either exact travel time or enough equations involving distance and speed must be available.
Updated On: Jun 12, 2026
- Statement I alone is sufficient, but Statement II alone is not sufficient.
- Statement II alone is sufficient, but Statement I alone is not sufficient.
- Both statements together are sufficient, but neither statement alone is sufficient.
- Even both statements together are not sufficient.
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The Correct Option is D
Solution and Explanation
Concept:
Distance is related to speed and time through the fundamental relation
\[
\text{Distance}=\text{Speed}\times \text{Time}.
\]
To determine a unique distance, sufficient information about speed and travel time must be available.
Step 1: Analyze Statement (I). We are told that the cyclist takes one hour more in one direction than in the opposite direction. This merely indicates that the effective speeds in the two directions are different, possibly due to slope, wind, road conditions, etc. For example, \[ 20 \text{ km in } 2 \text{ hr and } 1 \text{ hr} \] satisfies the condition. Also, \[ 100 \text{ km in } 10 \text{ hr and } 9 \text{ hr} \] also satisfies the condition. Hence the distance is not uniquely determined. Statement (I) alone is insufficient.
Step 2: Analyze Statement (II). Given: \[ \text{Speed}=10 \text{ kmph}. \] Knowing only speed is not enough because time is unknown. Distance cannot be determined. Statement (II) alone is insufficient.
Step 3: Combine both statements. Even after combining both statements, actual travel times in either direction remain unknown. The difference between the times is known, but their actual values are not. Hence infinitely many distances are possible. Therefore the distance cannot be uniquely determined.
Step 1: Analyze Statement (I). We are told that the cyclist takes one hour more in one direction than in the opposite direction. This merely indicates that the effective speeds in the two directions are different, possibly due to slope, wind, road conditions, etc. For example, \[ 20 \text{ km in } 2 \text{ hr and } 1 \text{ hr} \] satisfies the condition. Also, \[ 100 \text{ km in } 10 \text{ hr and } 9 \text{ hr} \] also satisfies the condition. Hence the distance is not uniquely determined. Statement (I) alone is insufficient.
Step 2: Analyze Statement (II). Given: \[ \text{Speed}=10 \text{ kmph}. \] Knowing only speed is not enough because time is unknown. Distance cannot be determined. Statement (II) alone is insufficient.
Step 3: Combine both statements. Even after combining both statements, actual travel times in either direction remain unknown. The difference between the times is known, but their actual values are not. Hence infinitely many distances are possible. Therefore the distance cannot be uniquely determined.
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