Ramesh is facing towards south direction. He rotates by 140 degrees in…

Concept: A facing direction can be written as a bearing measured clockwise from North — North = 0°, East = 90°, South = 180°, West = 270°, with the intercardinal directions midway (North-east = 45°, South-east = 135°, South-west = 225°, North-west = 315°). A clockwise turn adds to the bearing and an anti-clockwise turn subtracts from it, so a sequence of turns is simply a sum of signed angles, and any resulting bearing is reduced modulo 360° because a full circle brings the person back to the same facing. On a compass the eight named directions divide the circle into eight sectors of 45° each, so a named direction covers every bearing within 22.5° of its own value — North-west, for example, owns the whole sector from 292.5° to 337.5° around its central bearing of 315°. A final bearing is therefore reported as the named direction whose sector contains it, which is exactly what a question of this kind asks for.

Application to this question:

1. Initial facing is South, which is the bearing 180°.

2. First turn is 140° clockwise, so the bearing increases: 180° + 140° = 320°.

3. Second turn is 362° anti-clockwise, so the bearing decreases: 320° − 362° = −42°.

4. Reduce modulo 360° to bring the bearing into the 0°–360° range: −42° + 360° = 318°.

5. A bearing of 318° falls inside the North-west sector, which runs from 292.5° to 337.5°, sitting just 3° past its central bearing of 315°; no other sector contains it. The direction being faced is therefore North-west.

Cross-check: combine the two turns before applying them. Taking anti-clockwise as positive, the net turn is 362° − 140° = 222° anti-clockwise, and from South that gives 180° − 222° = −42° ≡ 318°. A third route uses the modulo idea on the turn itself: 362° anti-clockwise is one full circle plus 2°, so it is equivalent to a 2° anti-clockwise turn, and 320° − 2° = 318°. All three routes agree on 318°, i.e. North-west.

Contrast with the other named directions, each expressed as the net turn from South (180°) that would be needed to reach it:

• North-east is the bearing 45°, which needs a net 135° anti-clockwise (equivalently 225° clockwise) turn.

• East is the bearing 90°, which needs a net 90° anti-clockwise turn.

• West is the bearing 270°, which needs a net 90° clockwise turn.

Common slip: applying the net 222° turn in the clockwise sense instead of the anti-clockwise sense gives 180° + 222° = 402° ≡ 42°, a bearing that sits near North-east. The sense of every turn must be carried as a sign, not just as a size, and the two turns here are in opposite senses so they partly cancel.

Answer: Ramesh is facing North-west.