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Question

The town of Paranda is located on Green lake. The town of Akram is to the west of Paranda. Tokhada is to the east of Akram but to the west of Paranda. Kokran is east of Bopri but west of Tokhada and Akram. If they are all in the same district, which town is the farthest west?

The correct answer is

Bopri

Solving the Town Location Puzzle

This question asks us to determine which town is the farthest west based on the given information about their relative positions.

Let's break down each statement and represent the relationships between the towns. We will use the symbol '<' to mean 'is to the west of' or equivalently, '>' to mean 'is to the east of'.

  • "The town of Akram is to the west of Paranda."
    This can be written as: Akram < Paranda.
  • "Tokhada is to the east of Akram but to the west of Paranda."
    This means Tokhada is between Akram and Paranda. We can write this as: Akram < Tokhada and Tokhada < Paranda.
    Combining the first statement, we have: Akram < Tokhada < Paranda.
  • "Kokran is east of Bopri but west of Tokhada and Akram."
    This gives us two parts:
    • Kokran is east of Bopri: Bopri < Kokran.
    • Kokran is west of Tokhada: Kokran < Tokhada.
    • Kokran is west of Akram: Kokran < Akram.

Now, let's combine all the relationships we have:

  1. Akram < Tokhada < Paranda
  2. Bopri < Kokran
  3. Kokran < Tokhada
  4. Kokran < Akram

We want to find the town farthest west. This means we are looking for the town that is to the west of all other towns.

From relationship 4 (Kokran < Akram), we know Kokran is west of Akram.

From relationship 1 (Akram < Tokhada < Paranda), we know Akram is west of Tokhada and Paranda.

Since Kokran is west of Akram, and Akram is west of Tokhada and Paranda, Kokran must also be west of Tokhada and Paranda. (Kokran < Akram < Tokhada < Paranda).

Now let's consider Bopri. From relationship 2 (Bopri < Kokran), we know Bopri is west of Kokran.

Putting it all together, we have found the order from west to east:

Bopri < Kokran < Akram < Tokhada < Paranda

Therefore, the town that is the farthest west is Bopri.

Relative Positions of Towns
Statement Relationship (West < East)
Akram is west of Paranda Akram < Paranda
Tokhada is east of Akram Akram < Tokhada
Tokhada is west of Paranda Tokhada < Paranda
Kokran is east of Bopri Bopri < Kokran
Kokran is west of Tokhada Kokran < Tokhada
Kokran is west of Akram Kokran < Akram

Combining these relationships logically:
Kokran is west of Akram (Kokran < Akram).
Akram is west of Tokhada (Akram < Tokhada).
Tokhada is west of Paranda (Tokhada < Paranda).
So, Kokran < Akram < Tokhada < Paranda.
Bopri is west of Kokran (Bopri < Kokran).
Adding Bopri to the beginning of the sequence gives: Bopri < Kokran < Akram < Tokhada < Paranda.

The town at the leftmost side of this ordered sequence is Bopri.

Revision Table: Checking Town Positions

Town Order from West to East
Position (West to East) Town
1st (Farthest West) Bopri
2nd Kokran
3rd Akram
4th Tokhada
5th (Farthest East) Paranda

Based on the step-by-step analysis and the final ordering, Bopri is the town farthest to the west.

Additional Information: Understanding Relative Location Problems

Relative location problems are common types of spatial reasoning questions. They require you to understand directional terms like 'north', 'south', 'east', and 'west', and piece together multiple clues to determine the final arrangement or position of items.

Key strategies for solving such problems include:

  • Drawing a diagram or map to visualize the relationships.
  • Using symbols (<, >, =, etc.) to represent directional relationships on a single line (for east/west or north/south).
  • Breaking down complex sentences into simpler relationship statements.
  • Combining statements logically to build a complete picture.
  • Identifying the extreme points (farthest east, farthest west, etc.) once the order is established.

In this specific problem, we focused only on the east-west dimension. Other problems might involve north-south or even positions relative to landmarks like the Green lake mentioned for Paranda (though the lake wasn't needed to solve the relative east-west positions). The key is to isolate the relevant directional information and build the sequence step-by-step.

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Important Questions from Direction and Distance

  1. Vijendra walks a certain distance, say X metres, from his home towards the west. Then he turns left and walks 23 metres. After that, he turns left and walks 36 metres. Then he turns left again to walk 23 metres. He finally turns left and walks 18 metres to reach his home. Find the value of X.
  2. Gaurav exits from the backdoor of his north-facing house and walks 25 m straight, then he takes a left turn and walks 36 m, then he turns left and walks 47 m. He turns left again and walks 36 m. How far and in which direction is he from his house now?

  3. Reeta is standing facing south-east. First, she turns 135° clockwise. After that, she turns 90 °  anticlockwise. Then she turns 45 °  clockwise, followed by a 135 ° anticlockwise  turn. In which direction is she facing now?

  4. Sahasra started running from her house towards the north. After 40 meters she turned left and ran for 75 meters. She then turned right and ran for 30 meters, and again turned right to run 75 meters. In which direction was she running finally?

  5. At the time of sunset, Lopa and Kritika are sitting facing each other. If the shadow of Lopa falls to the right of Kritika, in which direction is Kritika facing?

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