Two trains A and B, moving at 45 km/h and 36 km/h respectively, cross a 1.2 km…
2024
Two trains A and B, moving at 45 km/h and 36 km/h respectively, cross a 1.2 km long bridge in 2 minutes and 3 minutes respectively. What is the ratio of the length of train A to the length of train B?
Answer: C. 1 : 2 — ConceptWhen a train completely crosses a bridge, the train's front travels the sum of the train length and the bridge length. Therefore, train length = speed…
- A.
1 : 3
- B.
2 : 3
- C.
1 : 2
- D.
2 : 1
Show answer & explanation
Correct answer: C
Concept
When a train completely crosses a bridge, the train's front travels the sum of the train length and the bridge length. Therefore, train length = speed × crossing time − bridge length. Use the same distance units before subtracting.
Application
Convert the speeds to kilometres per minute: train A travels 45 ÷ 60 = 0.75 km/min, and train B travels 36 ÷ 60 = 0.60 km/min.
In 2 minutes, the front of train A travels 0.75 × 2 = 1.50 km.
Hence, the length of train A is 1.50 − 1.20 = 0.30 km.
In 3 minutes, the front of train B travels 0.60 × 3 = 1.80 km; hence, the length of train B is 1.80 − 1.20 = 0.60 km.
Thus, the ratio of the lengths is 0.30 : 0.60 = 1 : 2.
Cross-check
Adding each train length back to the bridge length gives 1.50 km and 1.80 km. Dividing these distances by 0.75 km/min and 0.60 km/min gives the stated crossing times of 2 minutes and 3 minutes.
Therefore, the required ratio is 1 : 2.