Gaurav walks 20 metres towards North. He then turns left and walks 40 metres. He again turns left and walks 20 metres. Further, he moves 20 metres after turning to the right. How far is he from his or

Question

Gaurav walks 20 metres towards North. He then turns left and walks 40 metres. He again turns left and walks 20 metres. Further, he moves 20 metres after turning to the right. How far is he from his original position ?

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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.

Why the other options are wrong — (a) 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) 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) 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.

Concept: 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.

State PCS 2024 Q60 — Science & Technology PYQ with Answer

State PCS 2024 Q60 — Science & Technology PYQ with Answer