Question : A train travelling at the speed of $x$ km/hr crossed a 300 m long platform in 30 seconds and overtook a man walking in the same direction at 6 km/hr in 20 seconds. What is the value of $x$?
Option 1: 60
Option 2: 96
Option 3: 48
Option 4: 102
Correct Answer: 96
Solution :
According to the question,
Let the length of the train be $y$ m.
The speed of the train is $x$ km/hr.
A train travelling at the speed of x km/hr crossed a 300 m long platform in 30 seconds.
So, $x × \frac{5}{18}$ = $\frac{(y + 300)}{30}$
⇒ $x$ × $\frac{5}{18}$ = $\frac{y}{30}$+10
Also, the same train overtook a man walking in the same direction at 6 km/hr in 20 seconds
$(x-6) × \frac{5}{18}$ = $\frac{y}{20}$
In the above two equations, on eliminating $y$, we get
⇒ $x$ × $\frac{5}{18}$ = 20 × $(x-6) × \frac{5}{18}$ + 10
⇒ $x$ = 96
Hence, the correct answer is 96.
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