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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Question : A 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 $y$ is two-thirds that of $x$, then what is the length of $y$ (in m)?
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