A, B and C start from the same place and travel the same directions at speeds of 30, 40 and 60 km/hr respectively. B starts two hours after A. If B and C overtake A at the same instant, how many hours after A did C start.

Options

A. 3
B. 3.5
C. 4
D. 4.5

Answer

To solve the problem step by step, we will analyze the situation of A, B, and C based on their speeds and the time they start.

### Step-by-Step Solution:

1. **Identify the speeds of A, B, and C:**
- Speed of A = 30 km/hr
- Speed of B = 40 km/hr
- Speed of C = 60 km/hr

2. **Determine the time difference between A and B:**
- B starts 2 hours after A.

3. **Calculate the distance A travels before B starts:**
- Distance = Speed × Time
- Distance traveled by A in 2 hours = 30 km/hr × 2 hours = 60 km.

4. **Calculate the time taken by B to catch up with A:**
- When B starts, A is already 60 km ahead.
- The relative speed between B and A = Speed of B - Speed of A = 40 km/hr - 30 km/hr = 10 km/hr.
- Time taken by B to cover the 60 km = Distance / Relative Speed = 60 km / 10 km/hr = 6 hours.

5. **Determine the total time A has traveled when B overtakes A:**
- Since B takes 6 hours to catch up and started 2 hours after A, the total time A has traveled when B overtakes him = 2 hours + 6 hours = 8 hours.

6. **Set up the equation for C's travel:**
- C overtakes A at the same time as B. Therefore, we need to find out how long C takes to cover the same distance that A covers in 8 hours.
- Distance covered by A in 8 hours = Speed of A × Time = 30 km/hr × 8 hours = 240 km.

7. **Calculate the time taken by C to cover the same distance:**
- Let the time taken by C be t hours.
- Distance covered by C = Speed of C × Time = 60 km/hr × t hours.
- Set the distances equal: 60t = 240 km.

8. **Solve for t:**
- t = 240 km / 60 km/hr = 4 hours.

9. **Determine when C starts:**
- Since A has traveled for 8 hours when B and C overtake him, and C takes 4 hours to cover the same distance, C starts 4 hours after A.

### Final Answer:
C starts 4 hours after A.