Question

Manoj walks 5 m towards North, then turns to the East and walks 10 m. He turns right and walks 15 m, then turns left and walks 15 m. Which direction is he facing now?

• A. North
• B. East
• C. West
• D. South

Hint:

In direction sense problems, track facing direction after each turn: from East, right→South and left→North; from South, right→West and left→East.

Answer 1

The Correct Option is B

Start facing North and walk 5 m (facing North). Turn to East and walk 10 m (facing East). Turn right from East → facing South; walk 15 m. Turn left from South → facing East; walk 15 m. Final facing direction: East.

Answer 2

Direction problems like this are easiest to track by assigning a compass bearing to each leg and turning it by 90 degrees for every left or right instruction, rather than picturing the walk itself. Start Manoj facing North, which we can call a bearing of 0 degrees.

He walks 5 m North (bearing stays 0 degrees), then turns to face East, a 90-degree turn, so his bearing becomes 90 degrees, and he walks 10 m. Next, he turns right. A right turn always adds 90 degrees to the current bearing, so 90 + 90 = 180 degrees, which is South, and he walks 15 m facing South. Finally, he turns left. A left turn always subtracts 90 degrees from the current bearing, so 180 - 90 = 90 degrees, which is East again, and he walks 15 m facing East.

1. North: This would only be correct if the two later turns cancelled out perfectly to bring him back to his starting bearing of 0 degrees, but the right turn (+90) followed by the left turn (-90) actually returns him to 90 degrees (East), his bearing right after the first turn, not to 0 degrees.
2. East: Tracking the bearing step by step (0, then 90 after turning to East, then 180 after turning right, then 90 again after turning left) shows Manoj ends up facing 90 degrees, which is East.
3. West: West corresponds to a bearing of 270 degrees, which does not appear anywhere in the sequence of turns worked out above.
4. South: South, a bearing of 180 degrees, is where Manoj is facing right after the right turn, but the question asks for his direction after the final left turn, which shifts him another 90 degrees away from South.

Following the bearing through all three turns confirms Manoj ends the walk facing East.

Therefore, the correct answer is East.

Answer 3

Instead of tracking compass bearings in degrees, we can represent each facing direction as a small arrow, North as (0, 1), East as (1, 0), South as (0, -1), and West as (-1, 0), and use the rule that turning right rotates the arrow using \( (x, y) \to (y, -x) \), while turning left rotates it using \( (x, y) \to (-y, x) \). Manoj starts facing North, so his direction arrow is (0, 1), and he walks 5 m.

He then turns to face East, giving the arrow (1, 0), and walks 10 m. Next, he turns right: applying \( (x, y) \to (y, -x) \) to (1, 0) gives (0, -1), which is South, and he walks 15 m facing South. Finally, he turns left: applying \( (x, y) \to (-y, x) \) to (0, -1) gives (1, 0), which is East again, and he walks 15 m facing East.

1. North: North corresponds to the arrow (0, 1), which does not appear again anywhere after the first leg of the journey once the later turns are applied, so this cannot be his final facing.
2. East: Applying the rotation rule to each turn in sequence, (1,0) to (0,-1) on the right turn, then (0,-1) to (1,0) on the left turn, shows Manoj's arrow ends at (1, 0), which is East.
3. West: West corresponds to the arrow (-1, 0), which never appears in the sequence of rotations applied above.
4. South: South, the arrow (0, -1), is Manoj's direction right after the right turn, but the question asks for his direction after the subsequent left turn, which rotates the arrow again to (1, 0).

Tracking the direction as a rotating arrow through each turn confirms Manoj ends up facing East.

Therefore, the correct answer is East.