A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in metres) is :

### Concept & Formula Crossing a tunnel is mathematically identical to crossing a platform. The total distance covered is the train's length plus the tunnel's length. $$ \text{Length of Tunnel} = (\text{Speed} \times \text{Time}) - \text{Length of Train} $$ ### Step-by-Step Solution * **Given:** Train length = $800$ m, Speed = $78$ km/hr, Time = $1$ minute = $60$ seconds. * **Convert Speed:** $78 \times \frac{5}{18} = \frac{390}{18} = \frac{65}{3}$ m/s. * **Calculate Total Distance:** $\text{Distance} = \text{Speed} \times \text{Time} = \frac{65}{3} \times 60$. * Distance = $65 \times 20 = 1300$ meters. * **Find Tunnel Length:** $1300 \text{ m} - 800 \text{ m} = 500$ meters. ### Exam Strategy & Shortcut Keep terms in fractional form to allow for immediate simplification. Using $\frac{65}{3}$ against the $60$ seconds turns a potentially messy decimal multiplication into a clean $65 \times 20$. ### Common Pitfall Forgetting to convert $1$ minute into $60$ seconds, and multiplying the speed by $1$ instead. ### Final Answer Therefore, the correct answer is **500**.