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
Sunny drives 3 km towards west from point A. He then takes a right turn and drives 6 km. Again, he takes a right turn and drives 3 km. Finally, he takes a left turn and drives 3 km to reach point B. How far and towards which direction should he drive now in order to reach point A again?
One morning, Dhvani and Preet were sitting in a park facing each other. If Preet’s shadow fell to the left of Dhvani, then in which direction was Dhvani facing?
Udai walks 25 m towards the west, and then he turns left and walks 55 m. Then, he takes a right turn and walks 45 m. Then, he turns right again and walks 70 m. In which direction and what distance should he walk now to reach 15 m north of the starting point?
A cyclist travels towards the east for 2 km and then turns left to travel 1 km. From there, he turns left and travels another 800 metres to reach a tea junction. After a short break, he turns towards the south and travels for 500 metres. From there, he turns right and travels for 1.2 km. Finally, he tums right and travels for 1 km. In which direction is he from his starting position?
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?
One evening when Rosy was going to the market, she saw the Sun to her right. She walked for 100 metres and turned left and walked 50 metres to reach a crossroad. From there she walked towards the south for 40 Metres, and finally she turned left and walked 60 metres to reach the market. In which direction is the market from her house?
Reshma walked towards the south. After 500 m, she reached her friend Rehana's house. After meeting her friend, Reshma walked towards the east for 500 m, and then turned right and walked for another 500 m. From here, she turned right and walked for 1 km. Finally, she turned to her right and walked for 1 km to reach her college. In which direction is her college from Rehana's house?
Joya comes out of a bank and walks 14 m towards north. Then she turns left and walks 20 m. Then she turns left again and walks 36 m. Now she turns left and walks 65 m. In which direction should she turn now and what distance should she walk in order to reach a hospital that is 45 m in east of the bank ?
Starting from point Z, Khanna walked 80 m towards South. He took a left turn and walked 40 m. Then, he took a right turn and walked 40 m. Then, he took a left turn and walked 20 m, Again, he took a left turn and walked 120 m. How far and in which direction is Khanna now from the starting point Z?
Directions: Read the information given below carefully and answer the questions accordingly:
Rashmi stepped out of her college and walked 15 m towards South. She then took a left turn and walked 35 m to reach a pastry shop. She then took a right turn and walked 15 m. She then took a right turn and walked 35 m to reach her house. What is the approximate shortest distance between Rashmi's college and her house via the pastry shop?
Important Questions from Direction and Distance Turns
Starting from her home, a woman walks 10 km towards the west. She turns left and walks 25 km. Again she turns left and walks 10 km. After that, she again turns left and walks 5 km. How far is she from her house now?
A. 35
B. 20
C. 25
D. 40
Lalit walks 9 km east, turns left and walks another 8 km. He again takes a left and walks another 3 km. How far and in which direction is he now from his starting point?
A boy starts from his home northward in order to go to a hotel. He took right turn and took left to reach the hotel. Which direction is the hotel facing?
Arun went 6 m from his home towards south and turned left to cover 8 m. Again he turned left and covered 6 m. He again turned right and covered 4 m. What was the direct distance from his home and which direction was he facing?
Sri walked 4 km towards east from home to school, and he turned three times right side of 6 km respectively. What is the distance between his home and the school?
