Direction sense for IBPS PO

Direction questions go wrong in two places: a turn made the wrong way, and a final direction read from a messy sketch. The coordinate method removes both. You never picture a person turning; you only add and subtract numbers.

IBPS PO asks direction sense in three forms. The classic path ("walks 10 m north, turns right…"), the point-based puzzle ("Point A is 6 m north of B…"), which is now common in the mains, and coded directions, where symbols stand for "north of" or "east of". All three fall to the same method.

The coordinate method

Put the starting point at (0, 0).

• North adds to y, south subtracts from y.
• East adds to x, west subtracts from x.
• Straight-line distance from the start = √(x² + y²).
• Direction from the start: read the signs. +x and +y is north-east; +x and −y is south-east; −x and +y is north-west; −x and −y is south-west. If x = 0 or y = 0, the answer is a pure direction.

Common right triangles save time: 3-4-5, 6-8-10, 5-12-13, 8-15-17 and 7-24-25 (and their multiples, such as 15-20-25).

Turning

A right turn is 90° clockwise; a left turn is 90° anticlockwise. For angle questions, give each direction a bearing: north 0°, east 90°, south 180°, west 270°, with north-east 45°, south-east 135°, south-west 225° and north-west 315°. Add clockwise turns, subtract anticlockwise turns, and reduce the result to between 0° and 360°.

Worked example 1: a path

A person starts at P, walks 10 m north to Q, turns right and walks 6 m to R, turns right and walks 18 m to S, then turns left and walks 9 m to T. How far is T from P, and in which direction?

• P (0, 0) → north 10 → Q (0, 10).
• Right from north is east: 6 m → R (6, 10).
• Right from east is south: 18 m → S (6, −8).
• Left from south is east: 9 m → T (15, −8).
• Distance = √(15² + 8²) = √289 = 17 m. Signs +x, −y: south-east.

Worked example 2: a point-based puzzle

Point P is 6 m north of point Q. Point R is 8 m east of Q. Point S is 4 m south of R. Point T is 8 m west of S.

Put Q at (0, 0): P (0, 6), R (8, 0), S (8, −4), T (0, −4).

1. In which direction is T from Q? T lies straight south of Q: south, 4 m.
2. What is the distance between P and R? From P to R is 8 m east and 6 m south, so √(64 + 36) = 10 m.
3. In which direction is R from P? +x and −y: south-east.
4. What is the distance between P and T? Both have x = 0, and 6 − (−4) = 10 m.

Worked example 3: coded directions

In a code: A # B means A is 3 m north of B; A @ B means A is 4 m east of B; A $ B means A is 3 m south of B; A & B means A is 4 m west of B.

If P # Q @ R $ S, where is P with respect to S?

• Read it as three links: P # Q, Q @ R, R $ S.
• Start from the last letter: S (0, 0). R $ S puts R 3 m south: R (0, −3).
• Q @ R puts Q 4 m east of R: Q (4, −3).
• P # Q puts P 3 m north of Q: P (4, 0).
• Answer: P is 4 m east of S.

Worked example 4: turning by angles

A person faces north, turns 135° clockwise, then 90° anticlockwise, then 180°. Which way do they face?

• Start at 0°. 0 + 135 = 135°. 135 − 90 = 45°. 45 + 180 = 225°.
• 225° is south-west.

Worked example 5: shadows

In the morning, a person's shadow falls to their right. Which way are they facing?

• The morning sun is in the east, so shadows fall to the west.
• West is on the right of a person facing south.

Common mistakes

• Turning relative to the page instead of the person's current facing.
• Giving the direction backwards. "Direction of T from P" means stand at P and look at T.
• Adding distances along the path when the question asks for the straight-line distance.
• Dropping a sign when a move crosses the start line, such as going 10 north and then 18 south.
• Decoding a symbol chain in the wrong order. Each symbol links the two letters on either side of it.

Practice set

1. A person walks 3 km north, then turns right and walks 4 km. How far are they from the start, and in which direction?
2. Point A is 8 m east of point B. Point C is 6 m north of B. How far is C from A, and in which direction?
3. Facing west, a person turns right, then right again, then left. Which way do they face?
4. From P, a person walks 20 m south, turns left and walks 15 m. How far are they from P, and in which direction?
5. In the evening, a person's shadow falls directly behind them. Which way are they facing?
6. Facing east, a person turns 135° anticlockwise. Which way do they face?
7. Using the codes in worked example 3, if M $ N & O # K, where is M with respect to K?
8. A person walks 15 m south, turns right and walks 20 m, then turns right and walks 30 m. How far are they from the start, and in which direction?

Answers

1. 5 km, north-east. End point (4, 3); √(16 + 9) = 5.
2. 10 m, north-west. From A (8, 0) to C (0, 6) is 8 m west and 6 m north.
3. North. West, right to north, right to east, left to north.
4. 25 m, south-east. Left from south is east: (15, −20); √(225 + 400) = 25.
5. West. Evening shadows fall east, so the shadow is behind a person facing west.
6. North-west. 90° − 135° = −45°, which is 315°.
7. 4 m west of K. K (0, 0); O # K gives O (0, 3); N & O gives N (−4, 3); M $ N gives M (−4, 0).
8. 25 m, north-west. South 15 to (0, −15); right from south is west, 20 m to (−20, −15); right from west is north, 30 m to (−20, 15). √(400 + 225) = 25.

What to do next

• Learn the turning table and the five right triangles until you can recite them.
• Solve two point-based puzzles a day for a week, always starting from the most-mentioned point.
• Revise circular seating, where the same left-right discipline decides facing clues, and the reasoning plan for where direction fits in the section.