BPSC 70th CCE Prelims General Studies · Question 60 of 143

Correct — D, 60 metres. Put the walk on a grid with the starting point at the origin, north as the positive y direction and east as the positive x direction, and track the facing as well as the position — the facing is what the question is really testing. Gaurav starts facing north and walks 20 metres, reaching (0, 20). He turns left; a walker facing north who turns left is now facing west, so 40 metres takes him to (−40, 20). He turns left again; facing west, a left turn points him south, so 20 metres brings him to (−40, 0). Now the decisive step. He turns right while facing south, and for a walker facing south the right hand points west, not east. Twenty metres therefore carries him to (−60, 0). His finishing point is due west of where he began, because the two north–south legs cancel exactly — plus 20 then minus 20 — so no square roots are needed and the straight-line distance is simply 40 + 20 = 60 metres. The trap is built into option (a). A candidate who reads 'turns to the right' as though the compass rose were fixed, so that right means east, ends at (−20, 0) and answers 20 metres. That single misreading accounts for the presence of the smallest option in the list, and it is the error the whole item is designed to catch. Options (b) and (c) correspond to no coherent reading of the path at all; 40 metres is simply the longest single leg, and 30 metres is a middle value with nothing behind it.

• (a)20 metres — The result of treating the final right turn as though right always means east. Facing south, the walker's right is west, so the last leg carries him further from the start rather than back towards it. Anyone who ends at (−20, 0) has made exactly this error, and it is the single most common mistake in direction-sense questions.
• (b)40 metres — The length of the longest single leg, offered to catch a candidate who stops tracking after the second move or who assumes the answer must be one of the distances named in the stem. The final displacement is 60 metres, made up of the 40-metre westward leg plus the final 20 metres in the same direction.
• (c)30 metres — Corresponds to no reading of the path. It is a filler value placed between the two plausible answers to make the option set look like a graded range, and it can be dismissed as soon as you notice that every leg is a multiple of 20 and the north–south legs cancel.

Direction-sense questions test one idea and one idea only: left and right are defined relative to the person walking, not to the map. The four rules follow from that and are worth memorising as a block. Facing north, left is west and right is east. Facing south, left is east and right is west. Facing east, left is north and right is south. Facing west, left is south and right is north. Notice that the south-facing case reverses the intuition most people carry from looking at a map, and that is where almost every error occurs. The second idea in the question is the difference between distance travelled and displacement. Gaurav walks 20 + 40 + 20 + 20 = 100 metres in total, but the question asks how far he is from his original position, which is the straight-line displacement between start and finish — 60 metres. Where the intermediate legs cancel, as the two 20-metre north–south legs do here, the displacement collapses to simple addition along one axis; where they do not cancel, the displacement is the hypotenuse of a right triangle and Pythagoras is needed.

Work these on paper with coordinates rather than in your head, and record two things at every step: where he is and which way he is facing. Most wrong answers come from tracking the position correctly and losing the facing. A useful physical check is to point your pen in the direction of travel and rotate it at each turn — a left turn is anticlockwise, a right turn is clockwise, whatever direction you happen to be facing. Once the four positions are written down, ask before computing anything whether the intermediate legs cancel. Here the y-coordinates run 0, 20, 20, 0, 0, so the north–south motion nets to nothing and the whole answer lies along the x-axis; recognising that saves the arithmetic entirely. Finally, read the question's demand precisely. 'How far is he from his original position' asks for displacement. A differently worded stem — how far has he walked, or in which direction is he now facing — would have different answers from the same path, and BPSC sets all three variants.

• Left and right are relative to the walker's facing: facing north, left is west and right is east; facing south, left is east and right is west; facing east, left is north and right is south; facing west, left is south and right is north
• The four positions on this walk, with north as +y and east as +x, are (0, 0) → (0, 20) → (−40, 20) → (−40, 0) → (−60, 0)
• The two north–south legs cancel exactly, +20 then −20, so the finishing point lies due west of the start and the displacement is 40 + 20 = 60 metres with no Pythagoras required
• Total distance walked is 100 metres against a displacement of 60 metres — the question asks for the second, not the first
• Reading the last right turn as eastward instead of westward ends the walk at (−20, 0) and produces 20 metres, which is exactly option (a)

• Reading right and left against a fixed map instead of the walker's facing — the error that turns 60 metres into 20
• Answering the total distance walked, 100 metres, when the question asks how far he is from the start
• Tracking position but forgetting to update the facing after each turn, which makes the second and later turns unreliable

BPSC sets two or three reasoning items in the general studies paper and rotates direction sense through three shapes — final displacement, final facing, and direction of one point relative to another — and it plants the answer produced by a fixed-compass misreading among the options every time. UPSC does not set direction sense in General Studies Paper I; the skill belongs to the qualifying CSAT paper, where it appears alongside seating arrangements and series.

• practice — not a real PYQ

  A man walks 10 metres towards the south, turns left and walks 15 metres, then turns left again and walks 10 metres. In which direction is he facing now, and how far is he from his starting point ?

  • (a)Facing north, 15 metres away
  • (b)Facing north, 25 metres away
  • (c)Facing east, 15 metres away
  • (d)Facing south, 10 metres away

  Answer(a) Facing north, 15 metres away — from (0,0) he reaches (0,−10), then facing east he reaches (15,−10), then facing north he reaches (15,0), which is 15 metres due east of the start.

• practice — not a real PYQ

  A person facing west turns 90 degrees to his left, then 90 degrees to his right, and then 180 degrees. Which direction is he facing now ?

  • (a)North
  • (b)South
  • (c)East
  • (d)West

  Answer(c) East — facing west, a left turn gives south, a right turn from south gives west again, and a 180-degree turn from west gives east.