A train travels 20% faster than a car. Both start together from point A and move towards point B, which is 180 km away. They reach point B at the same time, but the train halts for a total of 30 minutes at intermediate stations. What is the speed of the train in km/hr?

Introduction / Context:
This question combines percentage-based speed comparison with equal arrival times and stoppage delays. The train is faster than the car by 20%, but it also wastes time in station halts. Since both vehicles start together and reach the destination at the same time, we can use the equality of their total journey times to determine the actual speeds.

Given Data / Assumptions:
- Distance from A to B = 180 km.
- Train speed is 20% faster than car speed.
- Car speed = c km/hr (unknown).
- Train speed = 1.2c km/hr.
- Train halts for a total of 30 minutes = 0.5 hours on the way.
- Both start together from A and arrive at B at the same time.

Concept / Approach:
The car travels continuously, so its total time is simply distance / speed. The train travels with a higher running speed but also accumulates 0.5 hours of stoppage time. Hence, total time for the train equals running time + 0.5. Since arrival times are equal, we set the car's travel time equal to the train's total time and solve for c, then compute the train's speed 1.2c.

Step-by-Step Solution:
Step 1: Let the car speed be c km/hr. Then the train speed is 1.2c km/hr.Step 2: Time taken by the car to travel 180 km = 180 / c hours.Step 3: Running time taken by the train without stops = 180 / (1.2c) hours.Step 4: Simplify 180 / (1.2c): 1.2c = (6/5)c, so 180 / (1.2c) = 180 * (5 / 6c) = 150 / c hours.Step 5: The train also stops for 0.5 hours, so total train time = 150 / c + 0.5 hours.Step 6: Since both arrive together, set car time equal to train time: 180 / c = 150 / c + 0.5.Step 7: Subtract 150 / c from both sides: (180 / c) - (150 / c) = 0.5, giving 30 / c = 0.5.Step 8: Solve for c: c = 30 / 0.5 = 60 km/hr.Step 9: Train speed = 1.2c = 1.2 * 60 = 72 km/hr.

Verification / Alternative check:
Check times using the found speeds. Car speed = 60 km/hr, so car time = 180 / 60 = 3 hours. Train speed = 72 km/hr, so running time = 180 / 72 = 2.5 hours. Including 0.5 hours of stops, total train time = 2.5 + 0.5 = 3 hours. Both times are equal, so the speeds are consistent with the problem statement.

Why Other Options Are Wrong:
56, 66, 84, and 60 km/hr give either too large or too small running times for the train. When you add the 0.5 hour stoppage, the train time will not match the car's time for those speeds. Only 72 km/hr simultaneously satisfies the 20% faster condition and the equal arrival time condition.

Common Pitfalls:
Some learners misinterpret "20% faster" as adding a fixed 20 km/hr instead of 20% of the car's speed. Others forget to add the 0.5 hour stoppage time to the train's running time. It is also easy to invert the ratio, mistakenly using c = 1.2 * train speed instead of train speed = 1.2c.

Final Answer:
The speed of the train is 72 km/hr.