BPSC 70th CCE Re-exam Prelims General Studies · Question 32 of 142

Correct — B, 10 metres. Put X at the origin of a grid and take the first leg as due north; the direction chosen does not matter, because every turn in the problem is a right turn and the shape is therefore fixed whichever way you start. Raj walks 80 metres north from X to Y, so Y is at (0, 80). He turns right, which now faces him east, and walks 50 metres to (50, 80). He turns right again, now facing south, and walks 70 metres to (50, 10). He turns right a third time, now facing west, and walks 50 metres to (0, 10). His final position is (0, 10) and his starting point is (0, 0), so he is 10 metres away — and the two points are on the same north-south line, so no square root is needed at all. The structure behind the arithmetic is worth seeing, because it makes the answer obvious without any coordinates. Four legs and three right turns trace a rectangle that almost closes. The two side legs are both 50 metres, one east and one west, so they cancel exactly and leave no east-west displacement. The two vertical legs are 80 metres north and 70 metres south, and they do not cancel: the gap between them, 80 minus 70, is 10 metres, and that is the entire answer. Whenever a direction-sense problem gives four legs with three same-hand turns, the distance from the start is simply the difference between the two opposite pairs — here the sideways pair cancels and the vertical pair differs by 10.

• (a)20 metres — The answer you get if the third leg were 60 metres instead of 70 — that is, the option produced by misreading one figure. It also tempts a candidate who has grasped that the answer is a difference of lengths but subtracts the wrong pair. The two 50-metre legs cancel; the difference that survives is 80 minus 70.
• (c)45 metres — Corresponds to no consistent reading of the moves at all. It is the decoy for a candidate who abandons the trace and estimates a plausible-looking middle value, and its presence is a reminder that on this item type a guess is worse than a blank on a negatively marked paper.
• (d)30 metres — Another arithmetically plausible but unsupported figure — it would arise from treating the sideways legs as unequal, or from subtracting 50 from 80. Since the two 50-metre legs are equal and opposite, they contribute nothing to the final displacement.

Direction-sense problems are coordinate geometry disguised as a story, and the reliable method is to make the disguise explicit. Fix the starting point at the origin, decide once which way is north, and track the position after each leg as a pair of coordinates. Right turns cycle the facing in the order north, east, south, west and back to north; left turns cycle it the other way. Displacement east and west are added and subtracted along one axis, north and south along the other, and the straight-line distance from the start is the hypotenuse of the two net displacements — the Pythagorean step, which is only needed when both net displacements are non-zero. The commonest configurations are worth recognising on sight: four legs with three same-hand turns give a near-rectangle, so the answer is a difference of two lengths; an L-shaped path with one turn gives a genuine right triangle, where the answer is a square root and the numbers are almost always a 3-4-5 or 5-12-13 triple.

Two disciplines make these safe under time pressure. The first is to draw, however roughly. A four-line sketch in the margin, with the lengths written on it, prevents the single commonest error in the whole item type — losing track of the facing after a turn, because 'turned right' is relative to the walker and not to the page. The second is to check whether the answer needs Pythagoras at all. Here it does not, because the east-west displacements cancel and the two points share a line; a candidate who reaches for the square root has misread the geometry and will waste twenty seconds. Notice also what the question does NOT ask. It asks how far Raj is from the starting point, not in which direction, and not how far he has walked. The total distance walked is 250 metres; the displacement is 10 metres; and the direction from X is due north. Papers of this kind routinely ask for the direction in a companion question, so it is worth reading the trace off the sketch before moving on.

• Coordinate trace with X at (0,0) and the first leg north: Y (0,80) → east 50 to (50,80) → south 70 to (50,10) → west 50 to (0,10). Distance from X = 10 metres.
• Right turns cycle the facing north → east → south → west → north; left turns cycle it in the reverse order.
• The two 50-metre legs are equal and opposite, so they cancel; the surviving displacement is the difference between the 80-metre and 70-metre legs.
• Total distance walked is 80 + 50 + 70 + 50 = 250 metres, while the displacement from the start is only 10 metres — the question asks for the second, not the first.
• Raj's final position lies due north of X, so a companion question asking for the direction would be answered 'north'.

• Losing the facing after a turn. 'Turned right' is relative to the walker, not to the page, so the direction must be recomputed at every turn.
• Reaching for Pythagoras when it is not needed. If one of the two net displacements is zero, the answer is simply the other one.
• Answering the total distance walked, 250 metres, instead of the distance from the starting point, which is 10 metres.

BPSC places three or four reasoning items directly in General Studies Paper-I, since the State prelims has no separate aptitude paper, and direction sense is a fixture — the 70th CCE paper of December 2024 carried an almost identical four-leg walk. Each carries the same one mark as a Bihar geography question and takes a fraction of the time, which makes them the highest-return items on the paper. UPSC keeps all of this in CSAT Paper-II, which is only qualifying at 33 per cent.

• practice — not a real PYQ

  A man walks 30 metres towards the east, then turns left and walks 40 metres. How far is he from his starting point ?

  • (a)50 metres
  • (b)70 metres
  • (c)10 metres
  • (d)35 metres

  Answer(a) 50 metres — the two legs are at right angles, so the displacement is the hypotenuse of a 30-40 right triangle, which is 50. This is the 3-4-5 triple that appears in these questions more often than any other.

• practice — not a real PYQ

  Starting from a point, a person walks 25 m north, then 15 m east, then 25 m south, then 5 m west. How far is he from the starting point and in which direction ?

  • (a)10 m east
  • (b)10 m west
  • (c)20 m east
  • (d)5 m east

  Answer(a) 10 m east — the north and south legs of 25 m cancel exactly, leaving a net east-west displacement of 15 m east minus 5 m west, which is 10 m east.