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 :
A. 4 : 3
B. 3 : 5
C. 3 : 4
D. 50 : 3
Answer: Option C
Solution(By Examveda Team)
$$\because $$ Distance covered by the truck in a minute = 550 metresThen, 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,
$$\eqalign{ & = \frac{{55}}{6}:\frac{{110}}{9} \cr & = \frac{1}{2}:\frac{2}{3} \cr & = {\bf{3}}\,\,\,\,\,{\bf{:}}\,\,\,\,\,\,{\bf{4}} \cr & (\text{Truck : Bus}) \cr }$$
$$\eqalign{ & {\bf{Alternate:}} \cr & {\text{Speed of truck}} = 550\,{\text{metres/min}} \cr & {\text{Speed of bus}} = \frac{{33}}{{45}}\,{\text{km/min}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{33000}}{{45}}\,{\text{metres/min}} \cr & {\text{Speed of truck}}:{\text{Speed of bus}} \cr & = 550:\frac{{33000}}{{45}} \cr & = 55:\frac{{3300}}{{45}} \cr & = 5:\frac{{300}}{{45}} \cr & = 1:\frac{{60}}{{45}} \cr & = 1:\frac{4}{3} \cr & = 3:4 \cr} $$
Related Questions on Speed Time and Distance
A. 48 min.
B. 60 min.
C. 42 min.
D. 62 min.
E. 66 min.
A. 262.4 km
B. 260 km
C. 283.33 km
D. 275 km
E. None of these
A. 4 hours
B. 4 hours 30 min.
C. 4 hours 45 min.
D. 5 hours
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