UPSC Prelims 2009 Q70: Science & Technology – Logical Reasoning & Puzzles
A person travels 12 km due North, then 15 km due East, after that 15 km due West and then
18 km due South. How far is he from the starting point ?
- (a) 6 km
- (b) 12 km
- (c) 33 km
- (d) 60 km
Answer: (a) 6 km
Explanation
A net-displacement direction puzzle
A person travels in four legs: 12 km North, 15 km East, 15 km West, 18 km South — we need the final straight-line distance from the start.
| Step | Net calculation |
|---|---|
| North-South leg | 12 km North − 18 km South = 6 km South (net) |
| East-West leg | 15 km East − 15 km West = 0 km (cancels out) |
| Final position | 6 km due South of the starting point |
Why the East-West legs cancel:
| Point | Detail |
|---|---|
| East and West distances | Equal (15 km each), so they exactly cancel out |
| Remaining net displacement | Only the North-South difference matters |
Answer: (a) 6 km.
Why each option is right or wrong
- (a) CORRECT. The equal East (15 km) and West (15 km) legs cancel out, leaving a net 6 km displacement (South).
- (b) Incorrect. 12 km doesn't account for the full net North-South displacement correctly.
- (c) Incorrect. 33 km would be the total distance travelled, not the net straight-line displacement.
- (d) Incorrect. 60 km vastly overstates the actual net distance from the starting point.
Key point
With equal East and West legs cancelling out, the net displacement is simply the North-South difference: 18 km South − 12 km North = 6 km South of the start.
Remember
12N, 15E, 15W, 18S: East-West cancels; net displacement = 6 km South of the start.
Common mistakes
- Adding up all four distances (total path length) instead of finding the net displacement.
- Forgetting that equal East and West legs cancel each other out completely.
- Making an arithmetic error in the final North-South subtraction.
Exam tip
For direction-displacement puzzles, cancel out equal opposite-direction legs first, then compute the remaining net distance.
Sources
- R. S. Aggarwal — A Modern Approach to Verbal and Non-Verbal Reasoning (Direction Sense Test)
- Arun Sharma — How to Prepare for Logical Reasoning for the CAT (direction and distance problems)