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 ?
- (a) An angle less than 45° South of East
- (b) An angle less than 45° North of East ✓ UPSC's answer
- (c) An angle more than 45° South of East
- (d) An angle more than 45° North of East
Why the answer is (b)
• The woman runs 12 km North and then 6 km South, resulting in a net displacement of 6 km North from the starting point.
• She then runs 8 km East, so her final position is 6 km North and 8 km East of the start.
• The direction is measured from the East axis towards the North, forming a right-angled triangle with the East leg as the base (8 km) and the North leg as the height (6 km).
• The angle θ with the East is calculated using tan(θ) = Opposite/Adjacent = 6/8 = 0.75.
• Since tan(45°) = 1 and 0.75 < 1, the angle θ is less than 45°.
• Therefore, she is located at an angle less than 45° North of East.
Why the other options are wrong
- (a) An angle less than 45° South of East
- The net displacement is North, not South, so the direction cannot be South of East.
- (c) An angle more than 45° South of East
- The net displacement is North, not South, so the direction cannot be South of East.
- (d) An angle more than 45° North of East
- The tangent of the angle is 0.75, which is less than 1, meaning the angle is less than 45°, not more.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2021, held on 10 October 2021. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.