'A' started from his house and walked 20 m towards East, where his friend 'B' joined him. They together walked 10 m in the same direction. Then 'A' turned left while 'B' turned right and travelled 2 m and 8 m respectively. Again 'B' turned left to travel 4 m followed by 5 m to his right to reach his office. 'A' turned right and travelled 12 m to reach his office. What is the shortest distance between the two offices ?
- (a) 15 m
- (b) 17 m ✓ UPSC's answer
- (c) 19 m
- (d) 20 m
Why the answer is (b)
• A starts at (0,0), walks 20 m East to (20,0), then 10 m East with B to (30,0).
• A turns left (North) and walks 2 m to (30,2); B turns right (South) and walks 8 m to (30,-8).
• B, facing South, turns left (East) and walks 4 m to (34,-8), then turns right (South) and walks 5 m to his office at (34,-13).
• A, facing North, turns right (East) and walks 12 m to his office at (42,2).
• The offices differ by 8 m East-West and 15 m North-South, so shortest distance = sqrt(8² + 15²) = 17 m, hence option (b).
Why the other options are wrong
- (a) 15 m
- 15 m is only the north-south separation between A's office at 2 m north and B's office at 13 m south, ignoring the 8 m east-west gap.
- (c) 19 m
- 19 m would require a 12 m east-west gap, but B's 4 m left move reduces A's 12 m eastward lead to an 8 m gap.
- (d) 20 m
- 20 m would come from using a 16 m east-west gap or adding the 8 m gap with the 12 m eastward leg, not from the actual 8 m by 15 m right triangle.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2019, held on 2 June 2019. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.