अरूण उत्तर की ओर 8 किमी. जाता है, और बाएँ मुड़कर 3 किमी . जाता है, और फिर पुनः दाएँ मुड़कर 4 किमी. और चलता है , फिर दाएँ मुड़ता है 3 किमी. और चलता है। आरंभिक बिन्दु से वह कितनी दूरी पर है ?

Options

A. 18 किमी
B. 14 किमी
C. 12 किमी
D. 16 किमी

Answer

**Step-by-Step Solution:**

1. **Starting Point:** Arun starts at a point which we will call Point O (the origin).

2. **First Move:** Arun moves 8 km to the North.
- New Position: Point A (0, 8) in coordinate terms (where the first value is the East-West position and the second value is the North-South position).

3. **Second Move:** Arun turns left (to the West) and moves 3 km.
- New Position: Point B (-3, 8).

4. **Third Move:** Arun turns right (to the North) and moves 4 km.
- New Position: Point C (-3, 12).

5. **Fourth Move:** Arun turns right again (to the East) and moves 3 km.
- New Position: Point D (0, 12).

6. **Final Position:** Now, we need to calculate the distance from the starting point (Point O) to the final position (Point D).
- The coordinates of Point O are (0, 0) and the coordinates of Point D are (0, 12).

7. **Distance Calculation:** The distance between two points in a straight line can be calculated using the formula:
\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, (x1, y1) = (0, 0) and (x2, y2) = (0, 12).
\[ \text{Distance} = \sqrt{(0 - 0)^2 + (12 - 0)^2} = \sqrt{0 + 144} = \sqrt{144} = 12 \text{ km} \]

**Final Answer:** Arun is 12 km away from the starting point.

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