Correct Answer - Option 4 : 200/3, 500/3
Given ∶
Time taken to cross a tree by train = 9 seconds
Speed of bike = 60 kmph
Time taken to cross the bike = 90 seconds
Formula Used ∶
Distance = Speed × Time
Calculation ∶
Case 1 ∶ Let the speed of the train be x km/hr or x × 5/18 m/sec
Time taken to cross a tree = 9 seconds
∴ Distance travelled = x × 5/18 × 9 = 5x/2 meter
So, length of the train = 5x/2 metres
Case 2 ∶ The speed of the bike = 60kmph
Relative speed of the train w.r.t bike = (x - 60) km/hr = (x - 60) × 5/18 m/sec
Time taken to cross the bike = 90 seconds
∴ Distance travelled = [(x - 60) × 5/18] × 90 = 25 (x - 60) meter
So, length of the train = 25 (x - 60) meter
Solving above equations, we get
5x/2 = 25 (x - 60)
⇒ x = 10x - 600
⇒ 9x = 600
⇒ x = 600/9 = 200/3 km/hr
Hence distance travelled = 5x/2 = (5/2) × (200/3) = 500/3 meter
∴ The speed of the train is 200/3 km/hr and the length of the train is 500/3 meter.