Question

The speeds of three cars are in the ratio 5 : 4 : 6. The ratio between the time taken by them to travel the same distance is :

Answer 1

$\mathbf{12:15:10}$

$\cline{1-}$

Let the speeds of the three cars be respectively 5x, 4x and 6x.

We may assume the three cars travel the same distance, say d, so to find the ratio between the times taken by them.

We know time = distance ÷ speed.  So, the ratio between the times will be

$\dfrac{d}{5x}:\dfrac{d}{4x}:\dfrac{d}{6x}$

On simplifying it by cancelling d/x from each, we get,

$\dfrac{1}{5}:\dfrac{1}{4}:\dfrac{1}{6}$

So this is the ratio, but it's in fractional form. We have to convert it in integral form.

For this, let's multiply each by the LCM of the denominators of each.

$\begin{tabular}{c|ccc}2&5,&4,&6\\ \cline{2-4}&5,&2,&3\\ \cline{2-4}\end{tabular}\quad\quad\quad\quad \text{LCM = 2\times 5\times 2\times 3=60 }$

So,

$\dfrac{1}{5}:\dfrac{1}{4}:\dfrac{1}{6}\ \implies\ \dfrac{1}{5}\times 60:\dfrac{1}{4}\times 60:\dfrac{1}{6}\times 60\ \implies\ \mathbf{12:15:10}$

Hence we got the ratio.