A train x running at 74 km/h crosses another train y running at 52 km/h in the opposite direction in 12 seconds. If the length of y is two-thirds that of x , then what is the length of y (in m)?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e 168.
Given:
Speed of train x = 74 km/h
Speed of train y = 52 km/h
Train x crosses train y in the opposite direction in 12 seconds.
Length of train y = 2/3 of the length of train x
Concept used:
(i) If the speed of body A is x and the speed of body B is y then the relative speed of the two bodies moving in opposite directions = (x + y)
(ii) 1 km/h = 5/18 m/s
Formula used:
Relative speed = Total length/Time taken to cross
Calculations:
Relative speed = Total length/Time taken to cross
⇒ (74 + 52)(5/18) = Total length/12
⇒ (126)(5/18) = Total length/12
Total length = 35 × 12 = 420 m
Let the length of train x be 3a.
So, length of train y = 2/3 × 3a = 2a
⇒ 2a + 3a = 420
⇒ 5a = 420
⇒ a = 84
Length of train y = 2a
⇒ 2 × 84 = 168 m
Thus, The length of train y is 168 m.