Question : Two trains 100 metres and 95 metres long, respectively pass each other in 27 seconds when they run in the same direction and in 9 seconds when they run in opposite directions. The speeds of the two trains are:
Option 1: 44 km/hr, 22 km/hr
Option 2: 52 km/hr, 26 km/hr
Option 3: 36 km/hr, 18 km/hr
Option 4: 40 km/hr, 20 km/hr
Correct Answer: 52 km/hr, 26 km/hr
Solution :
Let the speed of the first train be $x$ km/hr and the speed of the second train is $y$ km/hr.
Time = $\frac{\text{Total distance}}{{\text{Relative speed in same/Opposite direction}}}$
In the same direction,
⇒ $27=\frac{100+95}{(x-y)×\frac{5}{18}}$
⇒ $27=\frac{195×18}{5(x-y)}$
⇒ $x-y=26$ ----------------(i)
In the opposite direction,
⇒ $9=\frac{100+95}{(x+y)×\frac{5}{18}}$
⇒ $9=\frac{195×18}{5(x+y)}$
⇒ $x+y=78$ ------------------(ii)
Solving equation (i) and (ii), we get,
$x=52,$ and $y=26$
Hence, the correct answer is 52 km/hr and 26 km/hr.
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