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 speeds is

### Concept & Logic To find the ratio of speeds, both speeds must be expressed in the exact same units (e.g., meters per minute or kilometers per hour). $$Speed = \frac{Distance}{Time}$$ ### Step-by-Step Solution 1. **Calculate Truck's Speed:** * Distance = $550$ metres * Time = $1$ minute * Speed of truck = $550$ m/min. 2. **Calculate Bus's Speed:** * Distance = $33$ kms = $33,000$ metres * Time = $45$ minutes * Speed of bus = $\frac{33000}{45}$ m/min. * Simplifying: $\frac{33000 \div 15}{45 \div 15} = \frac{2200}{3} = 733.33$ m/min. 3. **Find the Ratio:** * Ratio = Speed of Truck : Speed of Bus * Ratio = $550 : \frac{2200}{3}$ * Multiply both sides by $3$ to remove the fraction: * Ratio = $1650 : 2200$ * Divide both sides by $500$ (or simplify step-by-step): * Divide by $550$: $1650 \div 550 = 3$ and $2200 \div 550 = 4$. * Ratio = $3 : 4$. ### Exam Strategy & Shortcut Instead of fully solving the division for the bus, keep it as a fraction. Ratio = $550 : \frac{33000}{45}$. Divide both sides by $550$: Ratio = $1 : \frac{60}{45}$ Simplify the fraction $\frac{60}{45}$ to $\frac{4}{3}$. Ratio = $1 : \frac{4}{3} \implies 3 : 4$. ### Common Pitfall Comparing speeds without converting them to the same unit first. If you compare $550$ directly with $\frac{33}{45}$, you will get a wildly incorrect ratio. ### Final Answer Therefore, the correct answer is **3 : 4**.