Question

Ram moves from a point \( X \) to 20 metres towards North. Then he moves 40 metres towards West. Then he moves 20 metres North. Then he moves 40 metres towards East and then 10 metres towards right and he reaches a point \( Y \). Find the distance and direction of \( Y \) from \( X \)?

• A. \( 30 \) metres, North
• B. \( 40 \) metres, North
• C. \( 30 \) metres, South
• D. \( 40 \) metres, South

Hint:

For direction problems, break movements into coordinate changes and use absolute distances.

Answer 1

The Correct Option is A

Step 1: Breaking down the movements.
- Ram starts at \( X \).
- Moves 20m North → Position: \( (0, 20) \).
- Moves 40m West → Position: \( (-40, 20) \).
- Moves 20m North → Position: \( (-40, 40) \).
- Moves 40m East → Position: \( (0, 40) \).
- Moves 10m to the right (South) → Position: \( (0, 30) \).
Step 2: Finding the distance from \( X \) to \( Y \).
Since \( Y \) is at \( (0,30) \) and \( X \) is at \( (0,0) \), \[ {Distance} = |30 - 0| = 30 { metres} \] Step 3: Finding the direction.
Since \( Y \) is directly above \( X \) on the Y-axis, the direction is North.
Thus, the correct answer is (A) 30 metres, North.