A 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:
Answer & explanation
Correct answer: option 3
Let length of train X = a meter & speed of train Y = S km/h
According to question ,
\(\frac{225 + a }{60 - S}\) = 72 ----(1)
in 2nd case ,
\(\frac{225 + a }{60 + S}\) = 18 ----(2)
Multiply equation 2 by 4
\(\frac{4(225 + a) }{60 + S}\) = 72 ----(3)
By observing equation 1 and 3
\(\frac{225 + a }{60 - S}\) = \(\frac{4(225 + a) }{60 + S}\)
4(60-S) = (60+S)
240 - 4S = 60 + S
180 = 5S
S = 36
So , Speed of train Y = 36 km/h
Length of train ,
\(\frac{(225 + a) }{60 - 36}\)= 72
225 + a = 72 × 24 km/h
225 + a = 72 × 24 ×\(\frac{(5) }{18}\)
a = 480 - 225
a = 255 m
So , length of train X = 225 m