If the wheel of the engine of a train $4 \frac{2}{7}$ metres in circumference makes 7 revolutions in 4 seconds, then the speed (in km/hr) of the train is

### Concept & Formula Speed is determined by the total distance covered divided by the time taken. The distance is the product of the circumference and the number of revolutions. Finally, convert the speed from m/s to km/hr. $$ \text{Distance} = \text{Circumference} \times \text{Revolutions} $$ $$ \text{Speed in km/hr} = \text{Speed in m/s} \times \frac{18}{5} $$ ### Step-by-Step Solution 1. **Given:** Circumference = $4 \frac{2}{7} \text{ m} = \frac{30}{7} \text{ m}$. Revolutions = $7$. Time = $4 \text{ s}$. 2. **Calculate the total distance covered:** Distance = $\frac{30}{7} \text{ m/rev} \times 7 \text{ rev} = 30 \text{ meters}$. 3. **Calculate the speed in m/s:** Speed = $\frac{\text{Distance}}{\text{Time}} = \frac{30}{4} = 7.5 \text{ m/s}$. 4. **Convert speed to km/hr:** Speed in km/hr = $7.5 \times \frac{18}{5} = 1.5 \times 18 = 27 \text{ km/hr}$. ### Exam Strategy & Shortcut Note the convenient numbers: the $7$ in the denominator of the fraction perfectly cancels the $7$ revolutions. The distance is exactly $30$ m. Speed = $30/4$ m/s. Multiply directly by $18/5$: $\left(\frac{30}{4}\right) \times \left(\frac{18}{5}\right) = \frac{6}{4} \times 18 = 1.5 \times 18 = 27$. ### Common Pitfall Forgetting the standard conversion factor from m/s to km/hr ($\frac{18}{5}$) forces you to manually calculate $3600/1000$, which consumes valuable exam time. ### Final Answer Therefore, the correct answer is **27**.