Two buses in opposite quadrants — Aptitude Question
Two buses in opposite quadrants: Two buses leave the same depot. One goes 30 km north then 40 km east; the other… Answer and worked solution on CodeKairo.
- Topic: Direction Sense
- Section: Logical Reasoning
- Difficulty: Hard
- Time target: 120 seconds
Question
Two buses leave the same depot. One goes 30 km north then 40 km east; the other goes 40 km south then 30 km west. How far apart are they?
Options
- 70 km
- 70√2 km
- 100 km
- 140 km
Show the answer and the worked solution
Correct answer: B. 70√2 km
Worked solution
- First bus ends at (40, 30); second at (−30, −40).
- Differences: 70 east–west and 70 north–south.
- Distance = √(70² + 70²) = 70√2 km (about 98.99 km).
Answer: 70√2 km.
The idea
Coordinates are safer than sketching once the paths bend more than once. Sum each axis, then apply Pythagoras to the differences.
Shortcut. East–west gap = 40 + 30 = 70 and north–south gap = 30 + 40 = 70; equal gaps make a square's diagonal, 70√2 km (≈ 99).
Common trap. "100 km" — seeing each bus 50 km from the depot (3-4-5) and adding 50 + 50, which assumes they went in exactly opposite directions.