To travel 720 km, an Express train takes 6 hours more than the Duronto train. If, however, the speed of the Express train is doubled, it then takes 2 hours less than the Duronto train to cover the same 720 km. What is the speed of the Duronto train (in km/h)?

Introduction / Context:
This is a two-variable time and speed problem involving two trains, Express and Duronto, travelling the same fixed distance under different speed conditions. The Express train is slower initially, taking 6 hours more than Duronto, but when its speed is doubled, it becomes faster and arrives 2 hours earlier than Duronto. Using these comparative time statements, we can form equations and solve for the speed of the Duronto train. Such questions are very common in railway aptitude and competitive exams.

Given Data / Assumptions:
- Distance travelled by both trains = 720 km.
- Let the speed of Duronto be v_D km/h.
- Let the speed of Express initially be v_E km/h.
- Express initially takes 6 hours more than Duronto: time_E1 = time_D + 6.
- When Express speed is doubled to 2v_E, its time becomes 2 hours less than Duronto: time_E2 = time_D - 2.
- Both trains run at constant speeds on the same route.

Concept / Approach:
We first express the travel times in terms of the speeds and the fixed distance using time = distance / speed. For Duronto, time_D = 720 / v_D. For the Express train, time_E1 = 720 / v_E. Doubling the Express speed leads to a new time time_E2 = 720 / (2v_E). Using the two given relationships between these times, we obtain two equations. Solving these, we find time_D first and then compute v_D as distance divided by time_D.

Step-by-Step Solution:
Step 1: Let time_D = 720 / v_D and time_E1 = 720 / v_E.From the first condition: time_E1 = time_D + 6.So 720 / v_E = 720 / v_D + 6. (Equation 1)Step 2: When Express speed is doubled, its time is time_E2 = 720 / (2v_E) = (1/2) * (720 / v_E) = (1/2) * time_E1.Given that time_E2 = time_D - 2, so (1/2) * time_E1 = time_D - 2. (Equation 2)Step 3: Use Equation 1 to rewrite time_E1 in terms of time_D: time_E1 = time_D + 6.Substitute into Equation 2: (1/2) * (time_D + 6) = time_D - 2.Step 4: Solve for time_D:(time_D / 2) + 3 = time_D - 2.Rearrange: 3 + 2 = time_D - time_D / 2 ⇒ 5 = time_D / 2 ⇒ time_D = 10 hours.Step 5: Now find v_D using time_D = 720 / v_D.So v_D = 720 / time_D = 720 / 10 = 72 km/h.

Verification / Alternative check:
With v_D = 72 km/h, time_D = 10 hours. From Equation 1, time_E1 = time_D + 6 = 16 hours, so v_E = 720 / 16 = 45 km/h. When Express speed is doubled to 90 km/h, its new time is time_E2 = 720 / 90 = 8 hours. Compare with Duronto: Duronto time = 10 hours. Indeed, 8 hours is 2 hours less than 10 hours, matching the second condition. Both conditions are satisfied, confirming v_D = 72 km/h is correct.

Why Other Options Are Wrong:
- A Duronto speed of 60 km/h would give time_D = 12 hours, which does not satisfy both relationships when you recompute Express times.
- Speeds such as 66 km/h or 78 km/h similarly fail either the “6 hours more” condition or the “2 hours less after doubling” condition.

Common Pitfalls:
Some candidates confuse which train is faster in each scenario and may swap the “more” and “less” conditions. Others try to guess speeds that “look nice” without forming proper equations, leading to inconsistent results. Carefully defining time_D and time_E1, translating the word statements literally into equations, and solving step by step is the most reliable method.

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