Question

The total distance covered by a train in a journey is 600 km and the total stoppage time of the train during the journey is 1 hour. The difference between the speed of the train when stoppage time is excluded and when stoppage time is included is 30 km/hr. What is the average speed of the train when stoppage time is included?

• A. 150 km/hr
• B. 90 km/hr
• C. 180 km/hr
• D. 120 km/hr

Answer 1

The Correct Option is D

Train Speed Calculation 

Step 1: Understanding the Problem

- Let the speed of the train without stoppage time be Sex and the speed of the train with stoppage time be Sin.

- The distance covered by the train is 600 km, and the difference in speed is 30 km/hr:

Sex - Sin = 30

Step 2: Time Calculation

- Using the formula for time:

$$\text{Time} = \frac{\text{Distance}}{\text{Speed}}$$

- When stoppage time is excluded:

$$T_{\text{ex}} = \frac{600}{\text{Sex}}$$

- When stoppage time is included:

$$T_{\text{in}} = \frac{600}{\text{Sin}}$$

- We know that the stoppage time is 1 hour:

$$T_{\text{in}} - T_{\text{ex}} = 1$$

Substituting the values of $T_{\text{ex}}$ and $T_{\text{in}}$:

$$\frac{600}{\text{Sin}} - \frac{600}{\text{Sex}} = 1$$

Step 3: Solving the Equation

Dividing both terms by 600:

$$\frac{1}{\text{Sin}} - \frac{1}{\text{Sex}} = \frac{1}{600}$$

From the earlier equation:

$$\text{Sex} = \text{Sin} + 30$$

Substituting this into the equation:

$$\frac{1}{\text{Sin}} - \frac{1}{\text{Sin} + 30} = \frac{1}{600}$$

Step 4: Solving for $\text{Sin}$

Solving the equation gives:

$$\text{Sin} = 120 \text{ km/hr}$$

Since $\text{Sex} = \text{Sin} + 30$, we have:

$$\text{Sex} = 120 + 30 = 150 \text{ km/hr}$$

Step 5: Conclusion

Conclusion: The average speed of the train when stoppage time is included is 120 km/hr.