train X travelling at 60 km/h overtakes another train Y, 225 m long, and completely passes it in 72 seconds. If the trains had been
going in opposite directions, they would have passed each other in 18 seconds. The length (in m) of X and the speed (in km/h) of
Y are, respectively:
This questions was previously asked in
SSC CGL 9th March 2020 Shift-2
245 and 54
Incorrect Answer255 and 40
Incorrect Answer255 and 36
Correct Answer245 and 45
Incorrect AnswerExplanation:
Time taken to cross in opposite direction = 18 second
Speed of train X = 60 km/hr = 60 \frac{5}{18}$$ = 16.66 m/sec
Length of train Y = 225 m
Let the length of train X be l m and speed of train Y be x m/sec.
Total length = (225 + l) m
Relative speed when trains run opposite direction = (16.66 + x) m/sec
Length = speed x time
225 + l = (16.66 + x) 18
225 + l = 300 + 18x
l = 75 + 18x ---(1)
Relative speed when trains run opposite direction = (16.66 - x) m/sec
225 + l = (16.66 - x) 72
225 + l = 1200 - 72x
l = 975 - 72x ---(2)
By eq(1) and (2),
75 + 18x = 975 - 72x
90x = 900
x = 10 m/sec
Speed (in km/h) of Y = 10 \frac{18}{5} = 36 km/hr
Put the value of x in eq(1)
l = 75 + 18 10 = 255 m
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By: santosh