A train takes 5 minutes to cross a telegraphic post. Then the time taken by another train whose length is just double of the first train and moving with same speed to cross a platform of its own length is (Hotel Management, 2007)

### Concept & Logic Time taken is directly proportional to the distance covered when the speed is constant. If we determine how many multiples of the original train's length need to be covered in the second scenario, we can multiply the base time by that factor. $$ \text{Time} \propto \text{Distance (at constant speed)} $$ ### Step-by-Step Solution * **Given (Train 1):** Let length be $L$ and speed be $S$. It takes $5$ minutes to cover distance $L$. * **Given (Train 2):** Length is double, so length = $2L$. Speed is $S$. * **Platform:** The platform is "of its own length" (meaning equal to Train 2's length), so platform length = $2L$. * **Total Distance for Train 2:** To cross the platform, Train 2 must cover its own length + platform length = $2L + 2L = 4L$. * **Calculate Time:** If covering distance $L$ takes $5$ minutes at speed $S$, covering distance $4L$ at the same speed will take $4 \times 5 = 20$ minutes. ### Exam Strategy & Shortcut Use proportional reasoning. First train length = $1$ unit (takes $5$ mins). Second train length = $2$ units. Platform length = $2$ units. Total crossing distance = $2 + 2 = 4$ units. Since $1$ unit takes $5$ mins, $4$ units take $4 \times 5 = 20$ mins. ### Common Pitfall Misinterpreting "of its own length" to mean the first train's length ($L$) rather than the second train's length ($2L$), which would incorrectly yield $3L$ distance and $15$ minutes. ### Final Answer Therefore, the correct answer is **20 minutes**.