Question

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

• A. 40
• B. 45
• C. 42
• D. 50

Answer 1

The correct option is A

40

Distance travelled by train = $480km$
Let the speed of the train be $xkmph$.

Time taken for the journey = $\frac{480}{x}$
Given speed is decreased by $8kmph$
Hence the new speed of train = $(x–8)kmph$

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

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

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

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

$\Rightarrow$ $1280=x^2–8x$

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

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

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

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

$\Rightarrow x-4=\pm 36$

Either $x=-32orx=40$

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

Thus, the original speed of the train is $40kmph$.