UPSC Prelims 2019 · CSAT
Question 57: Logical Reasoning and Mental Ability
'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 ?
AnswerUPSC’s answer is (b).
Take East as +x and North as +y, starting at (0, 0). A and B reach (30, 0) together. A turns left (north) 2 m to (30, 2), then right (east) 12 m to (42, 2). B turns right (south) 8 m to (30, -8), then left (east) 4 m to (34, -8), then right (south) 5 m to (34, -13). The offices differ by 8 east-west and 15 north-south: √(64 + 225) = 17 m.
Why each option is right or wrong
- (a) Wrong: 15 m is only the north-south gap.
- (b) Right: √(8^2 + 15^2) = 17 m.
- (c) Wrong: 19 m does not match offsets of 8 and 15.
- (d) Wrong: 20 m does not match offsets of 8 and 15.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2019, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.