A train travels a distance of $480 k m$ at a uniform speed. If the speed had been $8 k m / h r$ less, then it would have taken $3$ hours more to cover the same distance. The original speed of the train is ___ km/hr.

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Solution

The correct option is A
40

Distance travelled by train = $480 k m$
Let the speed of the train be $x k m p h$ .

Time taken for the journey = $\frac{480}{x}$
Given speed is decreased by $8 k m p h$
Hence the new speed of train = $(x - 8) k m p h$

Time taken for the journey = $\frac{480}{x - 8}$

According to the question,
$\frac{480}{x - 8} - \frac{480}{x} = 3$

$\Rightarrow$ $\frac{480 (x - x + 8)}{x (x - 8)} = 3$

$\Rightarrow$ $\frac{480}{3} \times 8 = x^{2} - 8 x$

$\Rightarrow$ $1280 = x^{2} - 8 x$

$\Rightarrow x^{2} - 8 x - 1280 = 0$

$\Rightarrow x^{2} - 8 x = 1280$

$\Rightarrow x^{2} - 2 \times x \times 4 + 16 = 1280 + 16$ (adding 16 on both sides)

$\Rightarrow (x - 4)^{2} = 1296$

$\Rightarrow x - 4 = \pm 36$

Either $x = - 32 o r x = 40$

As, speed cannot be a negative value,
we get $x = 40$

Thus, the original speed of the train is $40 k m p h$ .

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