A train overtakes two persons who are walking in the same direction in which the train is moving, at the rate of 2 kmph and 4 kmph respectively and passes them completely in 9 seconds and 10 seconds respectively. Find the length of the train.
a.50 m
b.40 m
c.60 m
d.70 m
e.None of these
Answers
Answer: 50 m
Explanation:
Let’s assume,
The speed of person 1 be “s1” = 2 km/hr = 2*(5/18) = 5/9 m/s
The speed of person 2 be “s2” = 4 km/hr = 4*(5/18) = 10/9 m/s
The train crosses person 1 & 2 completely in time “t1” = 9 s & “t2” = 10 s
Let the length of the train be “x” m and speed of the train be “y” m/s.
Equation 1: When the train crosses person 1 in the same direction
∴ x = (y - s1) * t1 ….. [∵ distance = speed * time]
⇒ x = (y – 5/9) * 9
⇒ x = 9y – 5
⇒ 9y – x = 5 ….. (i)
Equation 2: when the train crosses person 2 in the same direction
∴ x = (y – s2) * t2 ….. [∵ distance = speed * time]
⇒ x = (y – 10/9) * 10
⇒ x = 10y – 100/9
⇒ 90y – 9x = 100 ….. (ii)
On multiplying by 9 throughout eq. (i) and then subtracting it from eq. (ii), we get
9y = 55
⇒ y = (55/9) m/s ← speed of the train
Putting value of y in eq. (i), we get
9*(55/9) – x = 5
⇒ 55 – x = 5
⇒ x = 55 – 5 = 50 m
Thus, the length of the train is 50 meters.