Distance between two villages — Aptitude Question
Distance between two villages: Village A is 10 km north of B, and village C is 10 km east of B. Answer and worked solution on CodeKairo.
- Topic: Direction Sense
- Section: Logical Reasoning
- Difficulty: Medium
- Time target: 75 seconds
Question
Village A is 10 km north of B, and village C is 10 km east of B. What is the distance from A to C?
Options
- 10 km
- 10√2 km
- 20 km
- 14 km
Show the answer and the worked solution
Correct answer: B. 10√2 km
Worked solution
- AB and BC are perpendicular, each 10 km.
- AC = √(100 + 100) = √200 = 10√2 km (about 14.14 km).
Answer: 10√2 km.
The idea
Sketch the three points before computing. Equal perpendicular legs of length a give a diagonal of a√2.
Shortcut. AC must lie between 10 km and 20 km; 10√2 ≈ 14.14 is the exact value, while 14 km is only a rounding of it.
Common trap. "20 km" — adding AB and BC as if the road ran through B, rather than taking the straight line from A to C.