किसी रेलगाड़ी T की चाल 100 km प्रति घंटा है और एक व्यक्ति P की चाल 4 km प्रति घंटा है। यदि P, T की गति की दिशा में चलता है, तो T, P को 15 सेकंड में पार करती है। यदि P, T की विपरीत दिशा में चलता है, तो T, P को लगभग कितने सेकंड में पार करेगी?
सही उत्तर: (c) 13.85
रेलगाड़ी T की चाल = 100 km/h, व्यक्ति P की चाल = 4 km/h। जब P, T की दिशा में चलता है, तो आपेक्षिक चाल = 100 - 4 = 96 km/h = 96 x (5 / 18) = 80 / 3 m/s। 15 सेकंड में पार करती है, अतः रेलगाड़ी की लंबाई L = (80 / 3) x 15 = 400 मीटर। जब P विपरीत दिशा में चलता है, तो आपेक्षिक चाल = 100 + 4 = 104 km/h = 104 x (5 / 18) = 260 / 9 m/s। पार करने में लगा समय = 400 / (260 / 9) = 360 / 26 = 180 / 13 = 13.85 सेकंड।
In English (Question & Model Answer)
The speed of a train T is 100 km per hour and the speed of a person P is 4 km per hour. T crosses P in 15 seconds, if P travels along the direction of motion of T. If P travels along the opposite direction of T, then in how much time does T cross P, in seconds, approximately?
Correct Option: (c) 13.85
Let's calculate the time taken by train T to cross person P. Speed of train T (v_T) = 100 km/h. Speed of person P (v_P) = 4 km/h. When P travels along the direction of motion of T, the relative speed is v_same = 100 - 4 = 96 km/h. Converting 96 km/h to m/s: 96 x (5 / 18) = (96 x 5) / 18 = 480 / 18 = 80 / 3 m/s. The train crosses P in 15 seconds. Let L be the length of the train. Distance = Relative speed x Time => L = (80 / 3) x 15 = 80 x 5 = 400 meters. Now, if P travels along the opposite direction of T, the relative speed is v_opp = 100 + 4 = 104 km/h. Converting 104 km/h to m/s: 104 x (5 / 18) = 520 / 18 = 260 / 9 m/s. The time taken to cross P in the opposite direction is Time = Length / v_opp = 400 / (260 / 9) = 400 x (9 / 260) = (40 x 9) / 26 = 360 / 26 = 180 / 13 seconds. Calculating 180 / 13: 180 / 13 = 13.846... seconds, which is approximately 13.85 seconds.