Two trains start at the same time from stations X and Y, respectively, and…
2026
Two trains start at the same time from stations X and Y, respectively, and move towards each other. One train travels at a speed of 72 km/h, and the other at 48 km/h. At the point where they meet, the faster train has covered 96 km more than the slower train. What is the distance between stations X and Y?
Answer: D. 480 km — ConceptWhen two objects travel for the same duration, the ratio of the distances they cover equals the ratio of their speeds. If those distances are in the…
- A.
520 km
- B.
450 km
- C.
420 km
- D.
480 km
Attempted by 13 students.
Show answer & explanation
Correct answer: D
Concept
When two objects travel for the same duration, the ratio of the distances they cover equals the ratio of their speeds.
If those distances are in the ratio a:b, they may be written as ak and bk; the given difference then determines the common factor k.
Application
Reduce the speed ratio: 72:48 = 3:2.
Let the distances covered by the faster and slower trains be 3k km and 2k km, respectively.
Their difference is 3k - 2k = k. Since the difference is 96 km, k = 96 km.
The distance between X and Y is the sum of the two distances: 3k + 2k = 5k = 5 × 96 = 480 km.
Cross-check
The faster train covers 288 km in 288/72 = 4 hours, while the slower train covers 192 km in 192/48 = 4 hours. The times are equal, the difference is 96 km, and the total is 480 km.
Therefore, the distance between stations X and Y is 480 km.