Question : A train can cross a 1200-metre-long bridge completely in 16 seconds. It can cross a 1600-metre-long bridge completely in 20 seconds. What is the speed of the train?
Option 1: 360 km/hr
Option 2: 450 km/hr
Option 3: 540 km/hr
Option 4: 270 km/hr
Correct Answer: 360 km/hr
Solution :
Given,
Length of 1st bridge = 1200 m and time = 16 seconds
Length of 2nd bridge = 1600 m and time = 20 seconds
We know,
Distance = Speed × Time
Length of the 1st bridge = 1200m and time = 16 s
Distance = Length of the train + Length of the bridge
Now, Distance = Speed × Time
⇒ Length of the train + 1200 = Speed × 16
⇔ Length of the train = (16 speed – 1200).............(1)
Now, we have Length of the 2nd bridge = 1600m and time = 20 s
⇒ Distance = Length of the train + Length of the 2nd bridge
⇒ Distance = Length of the train + 1600
⇒ Distance = Speed × 20
⇒ Length of the train + 1600 = 20 $\times$ speed
From (1), we get,
⇒ 16 speed – 1200 + 1600 = 20 $\times$ Speed
⇒ 400 = 4 × speed
⇒ Speed = 100 m/s
⇒ Now, to convert m/s into km/h, we have to multiply the number by $\frac{18}{5}$
⇒ 100 m/s = 100 × $\frac{18}{5}$ = 360 km/hr
Hence, the correct answer is 360 km/hr.
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