A woman runs 12 km towards her North, then 6 km towards her South and then 8 km towards her East. In which direction is she from her starting point?
Answer & explanation
Answer: (b) An angle less than 45° North of East
She ends 6 km North and 8 km East of the start. Because the northward part (6) is smaller than the eastward part (8), she is North of East at an angle below 45°.
- Net North = 12 − 6 = 6 km; East = 8 km.
- She is 8 km East and 6 km North of the start.
- tan θ = 6/8 = 0.75, which is less than 1, so the angle from East towards North is less than 45° (about 36.9°).
Remember · Compare the two net components: the direction lies within 45° of the axis with the larger component.
Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·