A train crosses two persons, cycling in the same direction as the train in 12 and 18 seconds respectively. If the speeds of the two cyclists are 9 and 18 kmph respectively, find the length of the train एक ट्रेन अपनी ही दिशा में साइकिल चला रहे दो व्यक्तियों को क्रमशः 12 और 18 सेकेण्ड में पार करती है | यदि दो साइकिल चालकों की चाल क्रमशः 9 और 18 किमी./घंटा है, ट्रेन की लम्बाई ज्ञात कीजिये |

Let train length = L meters and train speed = V kmph. For first cyclist (9 kmph): Relative speed = (V - 9) kmph. Time = 12 seconds = 12/3600 hours. L = (V - 9) × 12/3600 × 1000 = (V - 9)/3. For second cyclist (18 kmph): Relative speed = (V - 18) kmph. Time = 18 seconds = 18/3600 hours. L = (V - 18) × 18/3600 × 1000 = (V - 18)/2. Equating: (V - 9)/3 = (V - 18)/2. Cross-multiplying: 2(V - 9) = 3(V - 18), giving 2V - 18 = 3V - 54, so V = 36 kmph. Then L = (36 - 18)/2 = 9 km = 90 meters. Verification with first cyclist: L = (36 - 9)/3 = 27/3 = 9 km = 90 meters. Both conditions are satisfied.