Understanding the Directional Reasoning Problem
This question asks us to find the final direction a person, Sumit, is facing after starting in a specific direction (north-east) and making a series of turns (clockwise and anticlockwise) by given angles.
To solve this directional reasoning problem, we need to keep track of Sumit's orientation after each turn, starting from his initial direction.
Step-by-Step Solution: Tracking Sumit's Directions
Let's break down the process by tracking Sumit's direction after each turn:
- Starting Direction: Sumit is initially facing North-east.
- First Turn: He turns 90° clockwise from North-east.
- North-east is exactly between North and East.
- A 90° clockwise turn from North-east moves him past East (45°) into the direction between East and South.
- The direction 90° clockwise from North-east is South-east.
- Second Turn: He turns 135° anticlockwise from South-east.
- Current direction is South-east.
- Turning anticlockwise from South-east: 45° takes him to East, another 45° takes him to North-east (total 90°), and another 45° takes him to North (total 135°).
- So, a 135° anticlockwise turn from South-east leads to North.
- Third Turn: He turns 90° clockwise from North.
- Current direction is North.
- Turning 90° clockwise from North leads directly to East.
Summary of Turns and Directions
We can summarize the sequence of directions:
| Step | Turn | Angle | Direction After Turn |
|---|---|---|---|
| Start | - | - | North-east |
| Turn 1 | Clockwise | 90° | South-east |
| Turn 2 | Anticlockwise | 135° | North |
| Turn 3 | Clockwise | 90° | East |
Final Direction
After all the turns, Sumit is facing East.
Revision Table: Key Concepts in Directional Reasoning
| Concept | Explanation | Relation to Problem |
|---|---|---|
| Cardinal Directions | North, South, East, West (90° apart) | Basis for all turns and orientations. |
| Intercardinal Directions | North-east, South-east, South-west, North-west (45° from nearest cardinal) | Starting direction was North-east. |
| Clockwise Turn | Rotation in the same direction as clock hands (e.g., North to East). | Used in the first and third turns. |
| Anticlockwise Turn | Rotation opposite to clock hands (e.g., North to West). | Used in the second turn. |
Additional Information: Solving Direction Problems
Solving directional reasoning problems involves visualizing or mentally tracking movement on a compass rose. Here are some tips:
- Understand the main directions (N, S, E, W) and sub-directions (NE, SE, SW, NW).
- Remember the angles between adjacent directions (90° between N and E, 45° between N and NE).
- Clearly distinguish between clockwise and anticlockwise turns.
- Break down large turns into smaller, easier steps (e.g., 135° = 90° + 45° or 3 x 45°).
- Consider net turns: If a person turns 90° clockwise and then 90° anticlockwise, they are back to the original orientation relative to the starting direction of the turn. In this problem, Sumit turned 90° clockwise, then 135° anticlockwise, then 90° clockwise. The net clockwise turn is 90° + 90° = 180°. The net anticlockwise turn is 135°. The final net turn is 180° clockwise - 135° anticlockwise = 45° clockwise from the starting direction (North-east). 45° clockwise from North-east is East. This confirms the step-by-step method.
Similar Questions
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?
Tamanna is walking towards the north from her house. After 500 metres she turns left and walks for 500 metres. Then she turns left and walks 250 metres to reach her friend’s house. In Which direction is her house from her friend’s house?
Starting from a point A, an animal walked 15 m towards East. It took a left turn and walked 25 m. Then, it took a right turn and walked 10 m. Again it took a left turn and walked 15 m. Finally, it took a left turn and walked 25 m. How far and in which directions is the animal now from the starting point A?
The length and breadth of a hall are 16 m and 13 m, respectively. A dog runs along all four walls once to catch the bone. How much total distance does the dog cover?
Gurman drove 28 km towards the West, took a left turn and drove 22 km. She then took a right turn and drove 18 km. She again took a right turn and drove 22 km. How far is she from starting point in a straight line?
Indira starts from point A, which is 7 km towards East of point B. From point A, she drives 4 km towards East. From here, she takes a left turn and drives 9 km. She then takes a left turn, drives 9 km and stops at point C. If from point C, Indira drives 9 km towards South, how far will she be from point B?
Nirav's house is 40 m south of Akash's house. Daksh's house is to the east of Akash's house in a straight line at a distance of X m. Prakash's house if to the west of Akash's house in a straight line at a distance of Y m. If the shortest distance between Prakash's house and Nirav's house is 50 m and the shortest distance between Daksh's house and Nirav's house is also 50 m, then what is the distance between Prakash's house and Daksh's house?
Kripal starts driving from his home and drives 37 km towards south. From there he turns left and drives 31 km. Then he turns right and drives 27 km. Then he turns left and drives a certain distance of Y km. After than, he turns left and drives 57 km. Now he finally turn left and drives 58 km to reach a bank, which is exactly 7 km south of his home. Find the value of Y in Km.
Starting from point X, a person walked 20 m towards South to reach point Y. From there, he took a left turn and walked 25 m to reach point Z. He then took a left turn and walked for another 20 m to reach point P. What is the approximate shortest distance between the points X and Z and in which direction is the person's final position with respect to point X?
Stepping outside her school, Katrina walked 40 m towards South to reach an ice - cream parlor. From there, she took a left turn and walked 15 m to reach a bus stop. She then took a left - turn and walked for another 30 m to reach the central park. What is the approximate shortest distance between the ice - cream parlor and the central park?
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?
