Direction TestMTP May 20Question 2222 of 165
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A man is facing towards East and turns through 45∘\displaystyle 45^\circ clockwise again 180∘\displaystyle 180^\circ clock-wise and then turns through 270∘\displaystyle 270^\circ anti-clock wise. In which direction is he facing now?

Options

ANorth
BNorth-East
CSouth
DSouth-West
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Correct Answer

✅ Option b — North-East

All Options:

  • ANorth
  • BNorth-East
  • CSouth
  • DSouth-West

Detailed Solution & Explanation

Let's represent the directions using standard angles where East is 0∘\displaystyle 0^\circ, North is 90∘\displaystyle 90^\circ, West is 180∘\displaystyle 180^\circ, and South is 270∘\displaystyle 270^\circ. Clockwise rotation corresponds to subtracting angles, and counter-clockwise (anticlockwise) rotation corresponds to adding angles.
1. **Initial State**: Facing East, which corresponds to an angle of 0∘\displaystyle 0^\circ.
2. **First Rotation**: Turns 45∘\displaystyle 45^\circ in the clockwise direction:
Angle1=0∘−45∘=−45∘\displaystyle \text{Angle}_1 = 0^\circ - 45^\circ = -45^\circ
3. **Second Rotation**: Turns 180∘\displaystyle 180^\circ in the clockwise direction:
Angle2=−45∘−180∘=−225∘\displaystyle \text{Angle}_2 = -45^\circ - 180^\circ = -225^\circ
4. **Third Rotation**: Turns 270∘\displaystyle 270^\circ in the anticlockwise direction:
Angle3=−225∘+270∘=45∘\displaystyle \text{Angle}_3 = -225^\circ + 270^\circ = 45^\circ

An angle of 45∘\displaystyle 45^\circ lies in the first quadrant, exactly halfway between East (0∘\displaystyle 0^\circ) and North (90∘\displaystyle 90^\circ). This corresponds to the North-East direction.

**Note on Typographical Error**: The textbook answer key incorrectly lists Option C (South) as the correct answer. As mathematically and geometrically proven above, the man is facing North-East. Therefore, North-East (Option B) is the correct answer.
Hence, **Option B** is the correct answer.

More Questions from Direction Test

A man stands on a point and starts walking towards North then turns left then turns right and then left in which direction he is moving.

Rahim started from point X and walked straight 5\displaystyle 5 km west, then turned left and walked straight 2\displaystyle 2 km, then again turned left and walked straight 7\displaystyle 7 km. In which direction is he from the point X?

Manu wants to go to the market. He starts from his house towards North and reaches a crossroad after 30\displaystyle 30m. He turns towards East, goes 10\displaystyle 10m till the second crossing and turns again, moves towards South straight for 30\displaystyle 30m where marketing complex exits. In which direction is the market from his house?

A man is facing North-West. He turns 90° in the clockwise direction, then 180° in the anticlockwise direction and then another 90° in the same direction. Which direction is he facing now?

Rajni walked 20 m towards the North. Then she turned right and walks 30 m. Then she turns right and walks 35 m. Then she turns left and walks 15 m. Finally she turns left and walks 15 m. In which direction and how many meters is she from the starting position?

At a crossing, there was a direction pole, which was showing all the four correct directions. But due to the wind, it turns in such a manner that now West pointer is showing South. Harish went in the wrong direction thinking that he was travelling East. In which direction he was actually travelling?

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