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
Two different positions of the same dice with faces K, B, V, M, P, and T are shown below. Select the letter that will be on the face opposite to the one having B.
Select the number from among the given options that can replace the question mark (?) in the following series.
3, 6, 9, 18, 21, ?
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Important Questions from Direction and Distance
Sita took an auto from her home in Andheri (A) to go to her college in Fatehpuri (F). Rather than continuing straight on the direct road to the college that had no turns, the auto driver took a diversion after 10 km and tumed right at Bandra (B) crossing, then at Colaba T- point (C) after 8 km turned left, again after covering 12 km turned left at Dalhousi Building (D) and soon after 8 km turned right at Elphinston point (E) and after covering 4 km reached Fatehpuri (F). Had the auto driver taken the direct route how much less distance would Sita have actually travelled between the starting point and the destination?
Radha walks a distance of 9 m towards the South-East. Then she walks 15 m towards the West. From here, she walks 9 m towards the North-West. Finally she walks 6 m towards the East and stands at the point. How far is she standing from the starting point?
According to the time by Nihaal's watch its half past one and the hour hand is pointing towards the north-east. Assuming that there is no change in Nihaal's position, in which direction would the minute hand point after 30 minutes?
According to the time by Rohan's watch, it is half past 6 and the watch's hands are pointing to the south. In which of the given directions will the minute-hand point AFTER exactly 24 hours?
According to the time by Rick's watch its quarter past eight. If the minute hand points towards the east, towards which direction would the hour hand point?
