A truck covers a distance of 550 metres in 1 minute whereas a bus covers a distance of 33 kms in 45 minutes. The ratio of their speed is :

Solution (By Examveda Team)

$$\because $$ Distance covered by the truck in a minute = 550 metres
Then, the speed of the truck will be :
$$\eqalign{ & \frac{{550 \to {\text{Metres}}}}{{60 \to {\text{Seconds}}}}\left\{ {{\text{Speed = }}\frac{{{\text{Distance}}}}{{{\text{Time}}}}} \right\} \cr & \left( {1{\text{ minute = 60 seconds}}} \right) \cr & = \frac{{550}}{{60}} \Rightarrow \frac{{55}}{6}{\text{ m/s}}.....{\text{(i)}} \cr} $$
Whereas, distance covered by the bus in 45 minutes = 33 km
Then, the speed of the bus will be :
$$\frac{{33{\text{ km}}}}{{45\min }} \Rightarrow \frac{{33 \times 1000}}{{45 \times 60}}$$

\[\left\{ \begin{gathered} 1{\text{ km = 1000 metres}} \hfill \\ {\text{1 min = 60 seconds}} \hfill \\ \end{gathered} \right\}\]

$$\eqalign{ \Rightarrow \frac{{110}}{9}{\text{ m/s}}.....{\text{(ii)}} \cr} $$
So, the ratio of their speeds will be,
$$\eqalign{ & = \frac{{55}}{6}:\frac{{110}}{9} \cr & = \frac{1}{2}:\frac{2}{3} \cr & = {\bf{3}}\,\,\,\,\,{\bf{:}}\,\,\,\,\,\,{\bf{4}} \cr & (\text{Truck : Bus}) \cr }$$

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$$\eqalign{ & {\bf{Alternate:}} \cr & {\text{Speed of truck}} = 550\,{\text{metres/min}} \cr & {\text{Speed of bus}} = \frac{{33}}{{45}}\,{\text{km/min}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{33000}}{{45}}\,{\text{metres/min}} \cr & {\text{Speed of truck}}:{\text{Speed of bus}} \cr & = 550:\frac{{33000}}{{45}} \cr & = 55:\frac{{3300}}{{45}} \cr & = 5:\frac{{300}}{{45}} \cr & = 1:\frac{{60}}{{45}} \cr & = 1:\frac{4}{3} \cr & = 3:4 \cr} $$