Train A travelling at 90 km/h overtake train B traveling in same direction in 15 seconds. Had train B travelled twice of its speed, than train A would have taken 45 seconds to overtake it. Find the length of train B given that its length is 50% of the length of train A. 90 किमी./घण्टे की चाल से जा रही ट्रेन A उसी दिशा में जा रही ट्रेन B को 15 सेकेण्ड में पार करती है। यदि ट्रेन B की चाल दोगुनी कर दी जाये तो अब ट्रेन A, ट्रेन B को 45 सेकेण्ड में पार करती है। ट्रेन B की लम्बाई बताइये यदि इसकी लम्बाई ट्रेन A की लम्बाई की 50 प्रतिशत है।

Let train A's speed be 90 km/h, train B's speed be v km/h, and lengths be La and Lb respectively. In same direction, relative speed = (90-v) km/h. Time = (La+Lb)/relative speed. First case: 15 = (La+Lb)/(90-v). Second case with 2v speed: 45 = (La+Lb)/(90-2v). From these: 15(90-v) = 45(90-2v). Dividing by 15: 90-v = 3(90-2v) = 270-6v. So 5v = 180, v = 36 km/h. Substituting: 15(90-36) = 15(54) = 810 m = La+Lb. Given Lb = 0.5 La, so La + 0.5La = 1.5La = 810, La = 540 m. Then Lb = 270 m. The answer 270 m is not among the options, making 'None of these' correct.