Two trains A and B were moving in opposite directions, their speeds being in the ratio 5 : 3. The front end of A crossed the rear end of B 46 seconds after the front ends of the trains had crossed each other. It took another 69 seconds for the rear ends of the trains to cross each other. The ratio of length of train A to that of train B is
Explanation:
Let the lengths of trains A and B be ‘A’ and ‘B’ and their speeds be ‘a’ and ‘b’ respectively.
Time taken for front end of A to cross rear end of B = 46 seconds
⇒ 46 = Ba+b
⇒ B = 46a + 46b …(1)
Total time taken for rear ends of the two train to cross each other = (46 + 69) = 115 seconds
⇒ 115 = A+Ba+b
⇒ A + B = 115a + 115b …(2)
(2) - (1)
⇒ A = 69a + 69b …(3)
Now, AB = 69(a+b)46(a+b) = 6946 = 32
Hence, option (b).
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