If a train runs at 40 kmph, it reaches its destination late by 11 minutes but if it runs at 50 kmph, it is late by 5 minutes only. The correct time for the train to complete its journey is

### Concept & Time Equivalence When distance is constant, $Speed \times Time$ is constant. Let the correct time be $t$ minutes. We equate the distance for both scenarios. $$S_1 \times T_1 = S_2 \times T_2$$ ### Step-by-Step Solution * **Given:** Speeds are $40$ kmph and $50$ kmph. * **Time Equivalence:** Let correct time be $t$ minutes. * Case 1 time = $(t + 11)$ minutes. * Case 2 time = $(t + 5)$ minutes. * **Calculation:** * $40 \times \frac{t + 11}{60} = 50 \times \frac{t + 5}{60}$ * $4(t + 11) = 5(t + 5)$ * $4t + 44 = 5t + 25$ * $t = 19$ ### Exam Strategy & Shortcut Difference in time = $11 - 5 = 6$ mins. Distance $D = \frac{40 \times 50}{50 - 40} \times \frac{6}{60} = \frac{2000}{10} \times \frac{1}{10} = 20$ km. Correct time = Time taken at 50 kmph - 5 mins. Time at 50 kmph = $\frac{20}{50}$ hrs = $\frac{2}{5} \times 60 = 24$ mins. Correct time = $24 - 5 = 19$ mins. ### Common Pitfall Misinterpreting "late by 11 mins" and "late by 5 mins" and adding them. Since both are "late", you must subtract the delay from the actual time taken to find the correct time. ### Final Answer Therefore, the correct answer is **19 min**.