Question

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

• A. 10 km
• B. 15 km
• C. 20 km
• D. 25 km

Hint:

Use coordinate method: treat movements as $(x,y)$ shifts to easily calculate final displacement.

Answer 1

The Correct Option is B

Concept: This is a direction and displacement problem. We track movement step-by-step and then find the straight-line distance from the final point to the starting point. Step 1:Start from home (origin).}

• Move 10 km South → Position: $(0, -10)$

Step 2:Turn right (from South → West), move 5 km: \[ (-5, -10) \]
Step 3:Turn right (from West → North), move 10 km: \[ (-5, 0) \]
Step 4:Turn left (from North → West), move 10 km: \[ (-15, 0) \]
Step 5:Final position: \[ (-15, 0) \] Home is at $(0,0)$.
Step 6: Distance to home: \[ \text{Distance} = 15 \text{ km} \]
Step 7: Final Answer: \[ \text{15 km} \]