 QUESTION

# A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. What is the length of the train?(a). 50 m(b). 150 m(c). 200 m(d). Data inadequate

Hint: Assume a variable for the length of the train. Write the equations relating the length of the train to the time taken to cross the pole and the platform and solve for the length of the train.

Let the length of the train be x meters.
It is given that the train takes 15 seconds to cross the pole.
The speed of the train is the ratio of distance traveled by train to the time taken by it. It is assumed to be constant.
${\text{Speed}} = \dfrac{{{\text{Distance}}}}{{{\text{Time}}}}$
Now, to cross past the pole, the train should cover a distance of x meters.
The speed of the train is then given as follows:
Speed = $\dfrac{x}{{15}}...........(1)$
Now, the time taken by the train to cross a platform of length 100 m is 25 seconds.
The distance covered by the train is (100 + x) meters. Then, we have:
Speed = $\dfrac{{x + 100}}{{25}}...........(2)$
Equating equations (1) and (2), we have:
$\dfrac{x}{{15}} = \dfrac{{x + 100}}{{25}}$
Cross multiplying, we have:
$25x = 15(x + 100)$
Simplifying, we have:
$25x = 15x + 1500$
Taking all terms containing x to the left-hand side of the equation, we have:
$25x - 15x = 1500$
Solving for x, we have:
$10x = 1500$
$x = \dfrac{{1500}}{{10}}$
$x = 150m$
Hence, the length of the train is 150 m.
Hence, the correct answer is option (b).

Note: The distance covered by the train to completely cross the platform is the sum of the length of the train and the platform and not the difference between them.speed is to be the same for given conditions.