Question : Train X running at 74 km/hr crosses another Train Y running at 52 km/hr in the opposite direction in 12 seconds. If the length of Train Y is two-thirds that of Train X, then what is the length of Train X (in m)?
Option 1: 210
Option 2: 200
Option 3: 252
Option 4: 168
Correct Answer: 252
Solution :
Speed of train X = 74 km/hr
Speed of train Y = 52 km/hr
Relative speed = 74 + 52 = 126 km/hr
= 126 × $\frac{5}{18}$
= 35 m/s
Time = 12 s
Total length = 35 × 12 = 420 m
So, the length of train Y = $\frac{2}{3}$ × the length of train X
⇒ The length of train X + the length of train Y = 420 m
⇒ The length of train X + $\frac{2}{3}$ × the length of train X = 420
⇒ $\frac{5}{3}$ × the length of train X = 420
⇒ The length of train X = 420 × $\frac{3}{5}$ = 84 × 3 = 252 m
Hence, the correct answer is 252 m.
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