Rohan walks 10 km towards north from a point A. Then he turns right and walks 6 km. Then, he again turns right and walks 10 km. In which direction is he now from the starting point?
East
Direction Reasoning Solution
This question involves understanding direction and distance based on a series of movements. We need to trace Rohan's path step-by-step from his starting point A and determine his final position relative to A.
Understanding Direction Changes
When a person turns 'right' or 'left', their facing direction changes. If someone is facing North:
- Turning Right makes them face East.
- Turning Left makes them face West.
Similarly, if someone is facing East:
- Turning Right makes them face South.
- Turning Left makes them face North.
And so on for other directions.
Tracing Rohan's Path from Point A
Let's break down Rohan's journey:
- Starting Point: Rohan starts at point A.
- First Movement: He walks 10 km towards North from point A. Let's call the end of this path point B. Point B is 10 km North of A.
- Second Movement: From point B, he turns right. Since he was heading North, turning right means he now faces East. He walks 6 km in this direction. Let's call the end of this path point C. Point C is 6 km East of point B.
- Third Movement: From point C, he again turns right. Since he was heading East, turning right means he now faces South. He walks 10 km in this direction. Let's call the end of this path point D. Point D is 10 km South of point C.
Final Position Analysis
Now let's determine the location of his final point D relative to his starting point A.
- Rohan moved 10 km North from A to B.
- Then he moved 6 km East from B to C.
- Finally, he moved 10 km South from C to D.
Consider the North-South movements. He moved 10 km North and then 10 km South. These two movements are opposite in direction and equal in magnitude (10 km). This means his final North-South position relative to his starting point A is the same as the North-South position of point B relative to point C, which is 0 difference. Point D is directly South of C, and C is directly East of B. Since the South movement (C to D) is equal to the North movement (A to B), point D will be at the same North-South level as A.
Consider the East-West movements. He moved 6 km East from B to C. There were no West movements. Point B is directly North of A. Point D is directly South of C. Since the North and South movements (10km each) cancel out vertically, point D is effectively 6 km East from a point directly North of A (which is B), but the vertical movement from B to D is 0 relative to A. This means point D is directly East of point A.
To visualize this: Imagine A is at coordinates (0,0). B is at (0, 10). C is at (6, 10). D is at (6, 0). His final position D (6,0) is 6 km East of his starting position A (0,0).
Therefore, Rohan is now in the East direction from his starting point A.
Revision Table: Rohan's Movement Summary
| Step | Starting Point | Movement Direction | Movement Distance | Ending Point Direction relative to previous point |
|---|---|---|---|---|
| 1 | A | North | 10 km | North of A (Point B) |
| 2 | B | Right Turn (East) | 6 km | East of B (Point C) |
| 3 | C | Right Turn (South) | 10 km | South of C (Point D) |
Final position D is 10 km South of C, which is 6 km East of B, which is 10 km North of A. The 10 km North and 10 km South movements cancel each other out vertically relative to A. Thus, D is 6 km East of A.
Additional Information on Direction and Distance
Direction and distance questions test your ability to follow instructions involving movement and turns. It's helpful to draw a diagram or visualize the path. Key concepts include:
- The four main directions: North, South, East, West.
- The four cardinal directions: North-East, North-West, South-East, South-West.
- Understanding what a 'right' or 'left' turn means relative to the current facing direction. A right turn is a 90-degree clockwise rotation, and a left turn is a 90-degree anti-clockwise rotation.
- Calculating the final position relative to the starting point by considering the net displacement in the North-South and East-West directions.
Important Questions from Direction and Distance Turns
After leaving school, Hemant and Anurag walk towards the north for 1 km to reach a bus stop. From the bus stop, Hemant turns left and walks for 500 m. Then he turns towards his left and walks for 2 km to reach his home. From the bus stop, Anurag turns right and walks for 250 m. Then he turns right and walks for 1 km to reach his home. In which direction is Anurag's home from Hemant's home?
A bank employee drives 10 km towards South from her house and turns to her left and drives another 20 km. She again turns left and drives 40 km, then she turns to her right and drives for another 5 km. She again turns to her right and drives another 30 km to reach her bank where she works. What is the shortest distance between her bank and her house ?
A woman runs 12 km towards her North, then 6 km towards her South and then 8 km towards her East. In which direction is she from her starting point ?
Two friends Xand Ystart running and they run together for 50 m in the same direction and reach a point. Xturns right and runs 60 m, while Yturns left and runs 40 m. Then Xturns left and runs 50 m and stops, while Yturns right and runs 50 m and then stops. How far are the two friends from each other now?
Shekhar starts walking south from his school and then took one right turn, one left turn and one right turn to reach his shop. In which direction is Shekhar with respect to his school?
