Question : A train passes by a lamp post on a platform in 7 seconds and passes by the platform completely in 28 seconds. If the length of the platform is 390 m, the length of the train (in metres) is:
Option 1: 120
Option 2: 130
Option 3: 140
Option 4: 150
Correct Answer: 130
Solution :
We have,
Length of the platform = 390 m
The time taken to cross a lamp post is 7 seconds.
The time taken to cross the platform is 28 seconds.
Let the length of the train be $x$ m.
Speed of the train = $\frac{\text{Distance}}{\text{Time}}$ = $\frac{x}{7}$ m/s
Length of the train + Length of the platform = Speed of train × Time
$⇒ x + 390 = \frac{x}{7} \times 28$
$⇒ x+390=4x$
$⇒ 3x=390$
$\therefore x=130$ m
Hence, the correct answer is 130.
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