Shashank walks a certain distance, say X m, towards the west, then turns left and walks 35 m, and then turns right and walks 18 m. From there, he turns left and walks 9 m, and then turns left again and walks 60 m. From there, he turns left and walks 9 m, and then turns left again and walks 12 m. He finally turns right and walks 35 m to reach a point that is exactly 10 m to the east of the starting point. What is the value of X?
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Understanding the Directional Walking Problem
This problem asks us to find an unknown initial distance Shashank walked based on a series of turns and distances, and his final position relative to his starting point. We can solve this by tracking his position using coordinates, assuming the starting point is the origin (0,0).
Step-by-Step Movement Analysis
Let's denote Shashank's position after each step. We'll use a coordinate system where East is positive x, West is negative x, North is positive y, and South is negative y.
- Starting Point: Let the starting point be $S = (0,0)$.
- Step 1: Walks $X$ m towards the west.
New position: $(-X, 0)$. - Step 2: Turns left (South) and walks 35 m.
New position: $(-X, 0 - 35) = (-X, -35)$. - Step 3: Turns right (West) and walks 18 m.
New position: $(-X - 18, -35)$. - Step 4: Turns left (South) and walks 9 m.
New position: $(-X - 18, -35 - 9) = (-X - 18, -44)$. - Step 5: Turns left (East) and walks 60 m.
New position: $(-X - 18 + 60, -44) = (42 - X, -44)$. - Step 6: Turns left (North) and walks 9 m.
New position: $(42 - X, -44 + 9) = (42 - X, -35)$. - Step 7: Turns left (West) and walks 12 m.
New position: $(42 - X - 12, -35) = (30 - X, -35)$. - Step 8: Turns right (North) and walks 35 m.
New position: $(30 - X, -35 + 35) = (30 - X, 0)$.
Final Position and Calculating X
The final position reached is $(30 - X, 0)$.
The problem states that this final point is exactly 10 m to the east of the starting point $(0,0)$. A point 10 m to the east of $(0,0)$ is $(10,0)$.
Therefore, we can equate the coordinates of the final position to $(10,0)$:
$(30 - X, 0) = (10, 0)$
Equating the x-coordinates, we get:
$$30 - X = 10$$
Now, we solve for $X$:
$$X = 30 - 10$$
$$X = 20$$
The value of $X$ is 20 meters.
Summary of Movements and Final Position
We can also track the net displacement in the East-West and North-South directions.
| Movement | Direction | Distance (m) | Change in X (m) | Change in Y (m) |
|---|---|---|---|---|
| Start | - | - | 0 | 0 |
| 1 | West | $X$ | $-X$ | 0 |
| 2 | South | 35 | 0 | $-35$ |
| 3 | West | 18 | $-18$ | 0 |
| 4 | South | 9 | 0 | $-9$ |
| 5 | East | 60 | $+60$ | 0 |
| 6 | North | 9 | 0 | $+9$ |
| 7 | West | 12 | $-12$ | 0 |
| 8 | North | 35 | 0 | $+35$ |
| Total Change | - | - | $-X - 18 + 60 - 12$ | $-35 - 9 + 9 + 35$ |
| $30 - X$ | 0 |
The total change in position is $(30 - X)$ in the x-direction (East) and 0 in the y-direction (North). The final position is $(30-X, 0)$ relative to the start $(0,0)$.
The problem states the final position is 10 m east of the start, which corresponds to the coordinate $(10,0)$.
Equating the x-coordinates: $30 - X = 10$, which gives $X = 20$. The y-coordinate is 0, which matches the final position description relative to the starting point.
Revision Table: Key Concepts in Direction Problems
| Concept | Description | How it Applies Here |
|---|---|---|
| Coordinate System | Representing position using (x, y) coordinates, typically with (0,0) as the start. | Used to track Shashank's position relative to his starting point. |
| Directions (North, South, East, West) | Standard compass directions. | Translate turns (left/right) into changes in direction and movement along axes. |
| Displacement vs. Distance | Displacement is the straight-line distance and direction from start to end. Distance is the total path length. | We used displacement (final position relative to start) to find X, not the total distance walked. |
| Relative Position | Describing one point's location based on another point. | The final position is described relative to the starting point. |
Additional Information: Solving Complex Direction Puzzles
Direction and distance problems often appear in reasoning tests. Using a coordinate system is a reliable method for tracking movements, especially when there are multiple turns and changes in direction. Here are some tips:
- Draw a Diagram: Sketching the path can help visualize the movements, although for complex paths like this one with an unknown distance, a coordinate approach is more precise.
- Break Down Movements: Analyze each step individually, determining the change in position (Δx, Δy) based on the direction and distance.
- Sum Changes: Add up all the Δx values to find the total change in the East-West direction and all the Δy values for the total change in the North-South direction.
- Final Position: The final position relative to the start is (ΣΔx, ΣΔy).
- Solve for Unknowns: If the final position is given, set the calculated final position coordinates equal to the given coordinates and solve the resulting equations.
Remember that turning left or right depends on the current facing direction. If you are facing West, a left turn is South, and a right turn is North.
Similar Questions
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Important Questions from Direction and Distance
What is the direction of U with respect to P?
What is the shortest distance between R and T?
If a person walks 3m towards the North from point V, takes a right turn and walks for another 15m, which of the following points would he reach?
In which direction is Amit facing at point F?
What is the distance between the starting point and the end point?
