A postman was returning to the post office which was in front of him to the North. When the post office was 100 metres away from him, he turned to the left and moved 50 metres to deliver the last letter at Shanti Villa. He then moved in the same direction for 40 metres, turned to his right and moved 100 metres. How many metres was he away from the post office?

Options

A. 0
B. 90
C. 150
D. 100

Explanation

To solve the problem step-by-step, we will visualize the movements of the postman and calculate his final distance from the post office.

### Step 1: Initial Position
- The postman is facing North, and the post office is 100 meters away from him in the North direction.
- We can represent this position as follows:
- Postman (P) is at point A (0, 0).
- Post Office (PO) is at point B (0, 100).

### Step 2: First Turn (Left)
- The postman turns left (to the West) and moves 50 meters.
- After moving 50 meters to the West, his new position (C) will be:
- C = (-50, 0)

### Step 3: Move in the Same Direction
- He continues moving in the same direction (West) for another 40 meters.
- His new position (D) will be:
- D = (-50 - 40, 0) = (-90, 0)

### Step 4: Turn to the Right
- Now, he turns to his right (which is now facing North) and moves 100 meters.
- His new position (E) will be:
- E = (-90, 0 + 100) = (-90, 100)

### Step 5: Calculate Distance from the Post Office
- Now, we need to find the distance from point E (-90, 100) to the post office at point B (0, 100).
- The distance formula between two points (x1, y1) and (x2, y2) is given by:
\[ \text{Distance} = \sqrt{(x2 - x1)^2 + (y2 - y1)^2} \]
- Substituting the coordinates:
\[ \text{Distance} = \sqrt{(0 - (-90))^2 + (100 - 100)^2} \]
\[ = \sqrt{(90)^2 + (0)^2} = \sqrt{8100} = 90 \text{ meters} \]

### Final Answer
The postman is 90 meters away from the post office.

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