One day, Ravi left home and cycled 10 kms southwards, turned right and cycled 5 kms and turned right and cycled 10 kms and turned left and cycled 10 kms. How many kilometres will he have to cycle to reach his home straight ?

Options

A. 10 kms
B. 15 kms
C. 20 kms
D. 25 kms

Explanation

To solve the problem step by step, we will track Ravi's movements and calculate the distance he needs to cycle to return home.

### Step 1: Starting Point
- Ravi starts at his home, which we can denote as point O.

### Step 2: First Movement
- He cycles **10 km south** from point O to point A.
- **Position of A:** (0, -10) (assuming O is at (0, 0))

### Step 3: Second Movement
- He then turns **right** (which is to the west) and cycles **5 km** to point B.
- **Position of B:** (-5, -10)

### Step 4: Third Movement
- Next, he turns **right** again (now facing north) and cycles **10 km** to point C.
- **Position of C:** (-5, 0)

### Step 5: Fourth Movement
- Finally, he turns **left** (now facing west) and cycles **10 km** to point D.
- **Position of D:** (-15, 0)

### Step 6: Calculate Distance to Home
- Now, we need to find the straight-line distance from point D back to point O.
- The coordinates of O are (0, 0) and the coordinates of D are (-15, 0).
- The distance can be calculated using the distance formula:
\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Plugging in the coordinates:
\[ \text{Distance} = \sqrt{(-15 - 0)^2 + (0 - 0)^2} = \sqrt{(-15)^2} = \sqrt{225} = 15 \text{ km} \]

### Conclusion
Ravi will have to cycle **15 km** to reach his home straight.

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