The length of Train D is L meters. It takes the same time to cross a 280-meter-long platform as Train E, whose length is (L + 140) meters, takes to cross a 620-meter-long platform. If the ratio of the speeds of Train D to Train E is 5 : 9, find the value of
L.

ATQ, Length of Train D = L meters. Length of platform crossed by Train D = 280 meters. Distance covered by Train D = L + 280. Length of Train E = L + 140 meters. Length of platform crossed by Train E = 620 meters. Distance covered by Train E = L + 140 + 620 = L + 760. Both trains take the same time. So, distance ratio = speed ratio. Speed ratio of Train D to Train E = 5 : 9. Therefore, (L + 280) : (L + 760) = 5 : 9. Cross multiply: 9 × (L + 280) = 5 × (L + 760). 9L + 2520 = 5L + 3800. 9L − 5L = 3800 − 2520. 4L = 1280. L = 1280/4. L = 320.