A person climbs a hill in a straight path from point ‘O’ on the ground in the direction of north-east and reaches a point ‘A’ after travelling a distance of 5 km. Then, from the point ‘A’ he moves to point ‘B’ in the direction of north-west. Let the distance AB be 12 km. Now, how far is the person away from the starting point ‘O’ ?
- (a) 7 km
- (b) 13 km ✓ UPSC's answer
- (c) 17 km
- (d) 11 km
Why the answer is (b)
• North-east and north-west are at right angles to each other, so OA (5 km) and AB (12 km) form a right angle at A.
• OB is the hypotenuse: OB² = 5² + 12² = 25 + 144 = 169.
• So OB = 13 km.
• Hence 13 km, option (b).
Why the other options are wrong
- (a) 7 km
- 7 km is the result of incorrectly subtracting the two distances (12 - 5) instead of using the Pythagorean theorem for perpendicular vectors.
- (c) 17 km
- 17 km is the result of incorrectly adding the two distances (12 + 5) instead of recognizing the right-angled triangle formed by the perpendicular directions.
- (d) 11 km
- 11 km is an arbitrary value that does not correspond to any valid geometric calculation for the given distances and angles.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2016, held on 7 August 2016. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.