A bus travels 1st 150 km is one dimensional motion with 25 kmph, next 200 km with 50 kmph. What must its speed in last 150 km such that the net average speed for 500 km is 20 km/h

Options

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

Answer

To solve the problem, we need to determine the speed of the bus during the last 150 km of its journey so that the average speed for the entire 500 km is 20 km/h.

### Step-by-Step Solution:

1. **Identify the distances and speeds:**
- First segment: 150 km at 25 km/h
- Second segment: 200 km at 50 km/h
- Third segment: 150 km at speed \( V \) km/h (unknown)

2. **Calculate the total distance:**
- Total distance = 150 km + 200 km + 150 km = 500 km

3. **Set the average speed formula:**
- Average speed = Total distance / Total time
- Given average speed = 20 km/h

4. **Calculate the total time required for the average speed:**
- Total time = Total distance / Average speed
- Total time = 500 km / 20 km/h = 25 hours

5. **Calculate the time taken for the first two segments:**
- Time for the first segment (t1) = Distance / Speed = 150 km / 25 km/h = 6 hours
- Time for the second segment (t2) = Distance / Speed = 200 km / 50 km/h = 4 hours

6. **Calculate the time taken for the third segment:**
- Let the time for the third segment (t3) be \( t3 = \frac{150}{V} \) hours, where \( V \) is the speed in km/h.

7. **Set up the equation for total time:**
- Total time = t1 + t2 + t3
- 25 hours = 6 hours + 4 hours + \( \frac{150}{V} \)

8. **Combine the known times:**
- 25 = 10 + \( \frac{150}{V} \)

9. **Isolate \( \frac{150}{V} \):**
- \( \frac{150}{V} = 25 - 10 \)
- \( \frac{150}{V} = 15 \)

10. **Solve for \( V \):**
- Cross-multiply to find \( V \):
- \( 150 = 15V \)
- \( V = \frac{150}{15} = 10 \) km/h

### Final Answer:
The speed of the bus in the last 150 km must be **10 km/h** to achieve an average speed of 20 km/h over the entire 500 km.