Suresh traveled 1200 km by air, which was 2/5 of the entire trip. One-third was by car and the rest by train. What distance did he travel by train?

Introduction / Context:Fraction-of-whole travel problems require reconstructing total distance from a known fraction, then allocating the remaining portions accordingly.

Given Data / Assumptions:

• Air: 1200 km = 2/5 of total.
• Car: 1/3 of total.
• Train: remainder.

Concept / Approach:Let total distance be D. From 1200 = (2/5)D, compute D. Then compute the car portion and finally the train portion as D minus the other two.

Step-by-Step Solution:D = 1200 * (5/2) = 3000 km.Car distance = (1/3) * 3000 = 1000 km.Train distance = 3000 − 1200 − 1000 = 800 km.

Verification / Alternative check:Fractions check: 1200/3000 = 2/5 and 1000/3000 = 1/3, leaving 800/3000 = 4/15 for train; all parts sum to 1.

Why Other Options Are Wrong:1600, 1800, 400 km are misallocations of the remaining 3/5 distance after accounting for the air and car portions.

Common Pitfalls:Applying 1/3 to the remaining distance instead of the total; forgetting to subtract both known portions.

Final Answer:800 km