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
Correct Answer: 200
Solution :
Speed = $\frac{\text{Distance}}{\text{time}}$
Train ‘A’ requires 15 seconds to cross train ‘B’ of length 300 m.
Speed of train B = 36 km/hr = $36 \times \frac{5}{18}$ = 10 m/s
Distance covered by train B in 15 sec = $10\times 15$ = 150 m
Let the length of train A be $l$ and the Speed of A be $x$.
Time = $\frac{\text{Distance}}{\text{Speed}}$
So, $\frac{l+150}{x}$ = 15 ------------------(1)
Train ‘A’ requires 30 seconds to cross a 500 m long stationary train ‘C’
So, $\frac{l+500}{x}$ = 30 ------------------(2)
Now dividing equation (2) by (1)
$\frac{l+500}{l+150} = \frac{30}{15}$
⇒ $l+500 = 2\times(l+300)$
⇒ $l +500 = 2l +300$
⇒ $l = 200$ m
Hence, the correct answer is 200
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