A man travels a total distance of 480 km in 4 hours, partly by air and partly by train. If he had travelled the entire 480 km by air, he would have saved four fifths of the time he would have taken by train and would have arrived 2 hours earlier than he actually did. How many kilometres did he travel by train in the actual journey?

Introduction / Context:
This is a multi-step word problem involving two different modes of travel (air and train) and comparisons of hypothetical scenarios. It tests your ability to translate verbal conditions into mathematical equations involving distance, speed, and time. You also have to interpret a comparative statement about time saved as a fraction of another time. Such problems are considered higher level in aptitude tests because they require careful reading and algebraic reasoning.

Given Data / Assumptions:
- Total distance = 480 km.
- Actual total time taken for the mixed journey = 4 hours.
- If he had travelled all 480 km by air, he would have reached 2 hours earlier than he actually did, so the all-air time would have been 2 hours.
- The time saved by travelling entirely by air is four fifths of the time he would have taken if he had travelled the whole distance by train.
- Speeds of air travel and train travel are constant and positive.

Concept / Approach:
First, use the information about arriving 2 hours earlier to find the hypothetical all-air travel time. Then, interpret the statement about saving four fifths of the train time to relate the all-air time and the all-train time. From this, we find the speeds for air and train when they cover the full 480 km. Once we know these speeds, we set up an equation for the actual mixed journey: some distance x by air and the remaining 480 - x by train in a total of 4 hours. Solving this equation gives the distance travelled by train in the actual situation.

Step-by-Step Solution:
Step 1: Let T_train be the time to cover 480 km by train only and T_air be the time to cover 480 km by air only.We are told the man would arrive 2 hours earlier by air than in the mixed 4 hour journey, so T_air = 4 - 2 = 2 hours.Step 2: The time saved by choosing air over train is four fifths of T_train.Time saved = T_train - T_air = (4/5) * T_train.So T_train - T_air = (4/5) * T_train, which gives T_air = (1/5) * T_train.Step 3: Substitute T_air = 2 into T_air = (1/5) * T_train.2 = (1/5) * T_train, so T_train = 10 hours.Step 4: Compute speeds for air and train for the 480 km distance.Train speed v_train = 480 / 10 = 48 km/h.Air speed v_air = 480 / 2 = 240 km/h.Step 5: Let the actual distance travelled by air be x km, so the distance by train is 480 - x km.Total actual time is 4 hours, so:x / 240 + (480 - x) / 48 = 4.Step 6: Solve the equation: x / 240 + (480 - x) / 48 = 4.Multiply throughout by 240 to clear denominators: x + 5 * (480 - x) = 960.This gives x + 2400 - 5x = 960 ⇒ -4x = 960 - 2400 = -1440 ⇒ x = 360 km.Step 7: Distance by train = 480 - 360 = 120 km.

Verification / Alternative check:
Check the times with x = 360 km by air and 120 km by train. Time by air = 360 / 240 = 1.5 hours. Time by train = 120 / 48 = 2.5 hours. Total actual time = 1.5 + 2.5 = 4 hours, which matches the problem statement. Also, all-air travel takes 2 hours, which is indeed 2 hours less than 4 hours. For the all-train journey, time is 10 hours, and time saved by air is 10 - 2 = 8 hours, which is four fifths of 10 hours. Everything is consistent, so the calculation is correct.

Why Other Options Are Wrong:
- 80 km, 90 km, and 110 km do not satisfy the time equation x / 240 + (480 - x) / 48 = 4 when substituted as the train distance (480 - x). They lead to total times different from 4 hours.
- Only 120 km gives a consistent solution that satisfies all conditions of the problem.

Common Pitfalls:
Many candidates misread the statement about saving four fifths of the train time and set up an incorrect equation. Others incorrectly assume that 4 hours is the time for either all-air or all-train travel, which is not the case. Always define the times clearly for each scenario and translate proportional statements carefully. Working step by step with clear algebraic equations helps avoid confusion in such multi-condition word problems.

Final Answer:
The man travelled 120 km by train in the actual journey.