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
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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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