A train start 16 minute late from its destination if it travel with 10 km/hr faster than its normal speed then it will be on time at a distance of 80 km. Find the actual speed of the train? एक रेल अपने निर्धारित स्थान से 16 मिनट देरी से चलती हैं, यदि वह 10 किमी/घंटे की चाल से तेज़ चले तो 80 किमी की दूरी के बाद ये सही समय पर हो जाती हैं। ट्रेन की वास्तविक चाल ज्ञात कीजिये ?

The train is 16 minutes late initially. With increased speed (v + 10) for 80 km, it reaches on time. The 16 minutes saved means the time difference = 16/60 hours. So: 80/v - 80/(v+10) = 16/60 = 4/15. Simplify: 80(v+10 - v) / v(v+10) = 4/15, so 800 / v(v+10) = 4/15. Cross-multiply: 12000 = 4v(v+10) = 4v² + 40v, so 4v² + 40v - 12000 = 0, giving v² + 10v - 3000 = 0. Solving: v = [-10 ± sqrt(100 + 12000)]/2 = [-10 ± 110]/2, so v = 50 or v = -60. Speed must be positive, so v = 50 km/hr. This matches option A.