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 :

Answer: Option C

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

$$\left\{\begin{array}{c}1\text{ km = 1000 metres}\text{hfill}\\ \text{1 min = 60 seconds}\text{hfill}\end{array}\right\}$$

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

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$$\begin{array}{rl}& \mathbf{Alternate}:\\ & \text{Speed of truck}=550\text{metres/min}\\ & \text{Speed of bus}=\frac{33}{45}\text{km/min}\\ & =\frac{33000}{45}\text{metres/min}\\ & \text{Speed of truck}:\text{Speed of bus}\\ & =550:\frac{33000}{45}\\ & =55:\frac{3300}{45}\\ & =5:\frac{300}{45}\\ & =1:\frac{60}{45}\\ & =1:\frac{4}{3}\\ & =3:4\end{array}$$