Question : A train travelling at the speed of $x$ km/hr crossed a 300 m long platform in 30 seconds and overtook a man walking in the same direction at 6 km/hr in 20 seconds. What is the value of $x$?
Option 1: 60
Option 2: 96
Option 3: 48
Option 4: 102
Correct Answer: 96
Solution : According to the question, Let the length of the train be $y$ m. The speed of the train is $x$ km/hr. A train travelling at the speed of x km/hr crossed a 300 m long platform in 30 seconds. So, $x × \frac{5}{18}$ = $\frac{(y + 300)}{30}$ ⇒ $x$ × $\frac{5}{18}$ = $\frac{y}{30}$+10 Also, the same train overtook a man walking in the same direction at 6 km/hr in 20 seconds $(x-6) × \frac{5}{18}$ = $\frac{y}{20}$ In the above two equations, on eliminating $y$, we get ⇒ $x$ × $\frac{5}{18}$ = 20 × $(x-6) × \frac{5}{18}$ + 10 ⇒ $x$ = 96 Hence, the correct answer is 96.
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Question : A passenger train, 150 m long, is travelling at a speed of 36 km/hr. If a man is cycling in the direction of a train at 9 km/hr, the time taken by the train to pass the man is:
Option 1: 10 seconds
Option 2: 15 seconds
Option 3: 18 seconds
Option 4: 20 seconds
Question : A train 150 m long takes 20 seconds to cross a platform 450 m long. The speed of the train (in km/hr) is:
Option 1: 108 km/hr
Option 2: 100 km/hr
Option 3: 106 km/hr
Option 4: 104 km/hr
Question : A train crosses two persons travelling at 4 km/hr and 6 km/hr in the same direction in 12 sec and 14 sec, respectively. The speed of the train is ________.
Option 1: 18 km/hr
Option 2: 26 km/hr
Option 3: 20 km/hr
Option 4: 24 km/hr
Question : Train ‘A’ requires 15 seconds to cross train ‘B’ of length 300 m moving in the opposite direction at a speed of 36 km/hr. Further, train ‘A’ requires 30 seconds to cross a 500 m long stationary train ‘C’. Find the length (in m) of train ‘A’.
Option 1: 200
Option 2: 300
Option 3: 250
Option 4: 275
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
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