Question:
Instructions: Amit was driving in New Town, where all roads run either north-south or east-west, forming a grid. Roads are at a distance of 1 km from each other and are parallel.
After driving as stated in the previous question (3 km north, 3 km west, then 4 km south from his starting point), Amit did not return to his starting point but instead drove a further 4 km east and 1 km north. How far is he from his starting point?
Instructions: Amit was driving in New Town, where all roads run either north-south or east-west, forming a grid. Roads are at a distance of 1 km from each other and are parallel.
After driving as stated in the previous question (3 km north, 3 km west, then 4 km south from his starting point), Amit did not return to his starting point but instead drove a further 4 km east and 1 km north. How far is he from his starting point?
After driving as stated in the previous question (3 km north, 3 km west, then 4 km south from his starting point), Amit did not return to his starting point but instead drove a further 4 km east and 1 km north. How far is he from his starting point?
Show Hint
After the extra move the north-south offset cancels to zero, leaving only a 1 km east-west gap.
Updated On: Jul 15, 2026
- 5 km
- 4 km
- 1 km
- 7 km
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Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Recall the position before the extra move.
As found earlier, after driving 3 km north, 3 km west and 4 km south, Amit is at (-3, -1) relative to his start at (0, 0).
Step 2: Apply the further move.
He now drives 4 km east (+4 in x) and 1 km north (+1 in y). New position: \((-3+4,\,-1+1)=(1,0)\).
Step 3: Find the straight-line distance from the start.
Distance \(=\sqrt{(1-0)^2+(0-0)^2}=\sqrt{1}=1\) km.
Step 4: Final Answer.
Amit ends up exactly 1 km from his starting point, so option C is correct.
As found earlier, after driving 3 km north, 3 km west and 4 km south, Amit is at (-3, -1) relative to his start at (0, 0).
Step 2: Apply the further move.
He now drives 4 km east (+4 in x) and 1 km north (+1 in y). New position: \((-3+4,\,-1+1)=(1,0)\).
Step 3: Find the straight-line distance from the start.
Distance \(=\sqrt{(1-0)^2+(0-0)^2}=\sqrt{1}=1\) km.
Step 4: Final Answer.
Amit ends up exactly 1 km from his starting point, so option C is correct.
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