# Rajdhani Express leaves Delhi for Dehradun. It crosses a Sandalwood tree in 9 seconds and a KTM bike travelling in the same direction at 60 kmph in 9

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Rajdhani Express leaves Delhi for Dehradun. It crosses a Sandalwood tree in 9 seconds and a  KTM bike travelling in the same direction at 60 kmph in 90 seconds. Calculate the speed and the length of the train?
1. 300/9, 200/9
2. 200/7, 300/7
3. 300/7, 500/7
4. 200/3, 500/3

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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.