An ant starts from point 'O' moving 50m due east, then 50m `30^(@)` south of east, then 50m `30^(@)` of south of that direction and to continue to move 50m deviating in same sence by `30^(@)` each time until it returns to its original position. Total distance travelled by ant to reach initital point 'O' is :

Options

A. `400m`
B. `500m`
C. `600m`
D. `700m`

Explanation

To solve the problem step by step, we need to analyze the ant's movement and calculate the total distance traveled until it returns to its original position.

### Step 1: Understand the Ant's Movement
The ant starts at point O and moves in a specific pattern:
1. 50 m due east.
2. 50 m at an angle of 30° south of east.
3. 50 m at an angle of 30° south of the last direction.
4. This pattern continues, deviating by 30° each time.

### Step 2: Calculate the Total Number of Moves
The ant continues moving until it completes a full circle (360°). Since each move deviates by 30°, we can find the total number of moves by dividing 360° by 30°:
\[ \text{Number of moves} = \frac{360°}{30°} = 12 \]

### Step 3: Calculate the Distance for Each Move
Each move the ant makes is 50 m. Therefore, the total distance traveled by the ant can be calculated by multiplying the distance of each move by the total number of moves:
\[ \text{Total distance} = \text{Distance per move} \times \text{Number of moves} = 50 \, \text{m} \times 12 = 600 \, \text{m} \]

### Step 4: Conclusion
The total distance traveled by the ant to return to its original position O is 600 m.

### Final Answer
The total distance traveled by the ant to reach the initial point O is **600 m**.

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