A bank employee drives 10 km towards South from her house and turns to her left and drives another 20 km. She again turns left and drives 40 km, then she turns to her right and drives for another 5 km. She again turns to her right and drives another 30 km to reach her bank where she works. What is the shortest distance between her bank and her house ?

(a) 20 km
(b) 25 km ✓ UPSC's answer
(c) 30 km
(d) 35 km

Why the answer is (b)

• Take the house as (0,0), with east as +x and north as +y.

• 10 km south gives (0,-10); a left turn while facing south means east, so 20 km east gives (20,-10).

• A left turn while facing east means north, so 40 km north gives (20,30).

• A right turn while facing north means east, so 5 km east gives (25,30); a right turn while facing east means south, so 30 km south gives (25,0).

• The bank is 25 km east and 0 km north/south of the house, so the shortest distance is 25 km, option (b).

Why the other options are wrong

(a) 20 km: The final position is 25 km east of the house, not 20 km, because the eastward legs total 20 km + 5 km.
(c) 30 km: The final position is 25 km east of the house, not 30 km, because the northward and southward legs cancel to 0 km.
(d) 35 km: The final position is 25 km east of the house, not 35 km, because the net displacement is only the 25 km eastward distance.

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.