A driver leaves his village and first drives 20 km towards the North, where he stops for breakfast.\nHe then turns left and drives another 30 km to stop for lunch, again turns left and drives 20 km to stop for evening tea, and finally turns left once more and drives 30 km to reach the town where he has supper.\nAfter the evening tea halt, in which direction does he drive to reach the town?

Difficulty: Easy

Correct Answer: East

Explanation:


Introduction / Context:
This problem is a classic direction sense question where a person travels in straight lines and makes a sequence of left turns. We must carefully track his path step by step and identify the direction of his last stretch of travel. Although there are multiple halts (breakfast, lunch, evening tea and supper), what really matters is the direction he is facing before and after each turn, especially just after evening tea when he starts his final drive to the town.


Given Data / Assumptions:

  • The driver first drives 20 km towards the North from the village.
  • He then turns left and drives 30 km, stopping for lunch.
  • After lunch, he again turns left and drives 20 km, stopping for evening tea.
  • After evening tea, he turns left once more and drives 30 km to reach the town.
  • All turns are 90 degree left turns, and the roads are straight.
  • We use the usual convention: facing North, left is West; facing West, left is South; facing South, left is East.


Concept / Approach:
To determine the final direction, it is helpful to track both the directions of travel and the relative orientation after each turn. Every left turn changes the facing direction by 90 degrees anticlockwise. We can either draw a simple diagram or simulate the movements using coordinates, but here the key question is not the final position but specifically the direction of the last movement starting from the evening tea point. Once we know what direction he was facing at that moment, applying one more left turn gives the direction of the final leg.


Step-by-Step Solution:
Step 1: From the village, the driver travels 20 km towards the North, so at the breakfast stop he is facing North. Step 2: From facing North, he turns left. A left turn from North means he now faces West, and he drives 30 km to reach the lunch point. Step 3: At the lunch point, he is facing West. He turns left again, so he now faces South, and travels 20 km to reach the evening tea point. Step 4: At the evening tea point, he is facing South. The problem now asks for the direction of his drive after this stop. Step 5: From facing South, a left turn will make him face East (because turning left from South is equivalent to rotating 90 degrees anticlockwise, which points to East). Step 6: Therefore, his final drive from the evening tea halt to the town is in the East direction.


Verification / Alternative check:
We can verify the sequence by noting that three consecutive left turns effectively change a North-facing person to East-facing. Starting from North: first left gives West, second left gives South, and third left gives East. Because the driver makes these three left turns sequentially across the journey, his final direction of motion must be East. Drawing a simple square or rectangle with arrows labelled in order (North, West, South, East) will visually confirm the same pattern without any complicated calculations.


Why Other Options Are Wrong:
West would be the direction after only one left turn from North, which describes his movement to the lunch point, not the final leg. North is the initial direction, not the direction after three left turns. South is the direction he faces after the second left turn and is used for the leg between lunch and evening tea, not for the trip from evening tea to the town. North-East does not arise at any stage because all turns are exact right angles, so only the four main directions (North, East, South, West) appear in the path.


Common Pitfalls:
A common mistake is to mix up the number of left turns or to assume that three left turns bring a person back to the original direction, which is actually incorrect (four left turns return you to the original direction). Another error is to focus too much on distances to different stops instead of tracking orientation. Carefully listing the facing direction after each turn systematically avoids confusion and ensures that the final direction is identified correctly as East.


Final Answer:
After evening tea, the driver travels towards the East to reach the town.

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