A train running at a certain speed takes 20 seconds to cross a signal post and 50 seconds to cross a bridge. Which of the following statements is correct about the length of the bridge?

### Concept & Logic Because the train travels at a constant speed, the distance covered is directly proportional to the time taken. The time to cross the bridge comprises the time to cross the train's own length plus the time to purely cross the bridge's length. $$ \text{Distance} \propto \text{Time} $$ ### Step-by-Step Solution * **Given:** * Time to cross signal post (Train's length) = $20$ seconds. * Time to cross bridge (Train's length + Bridge's length) = $50$ seconds. * **Calculation:** * Time taken to cover *only* the bridge's length = Total time - Time for train's length. * Time for bridge's length = $50 - 20 = 30$ seconds. * Ratio of Bridge's length to Train's length = Ratio of respective times. * Ratio = $\frac{30}{20} = 1.5$. * Thus, the bridge is $1.5$ times the length of the train. ### Exam Strategy & Shortcut Avoid assigning variables like $x$ or $y$. Just look at the times: $20$s for the train, leaving $30$s for the bridge. $\frac{30}{20}$ is exactly $1.5$. ### Common Pitfall A standard error is dividing $50$ by $20$ to get $2.5$, which represents the ratio of the *total distance* to the train's length, not the *bridge's length* to the train's length. ### Final Answer Therefore, the correct answer is **1.5 times the length of the train**.