Question : Train B, speeding at 100 km/hr, crosses another train C, running in the same direction, in 2 minutes. If the lengths of trains B and C are 150 metres and 250 metres, respectively, what is the speed of train C (in km/h)?
Option 1: 75
Option 2: 88
Option 3: 95
Option 4: 110
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Correct Answer: 88
Solution :
Let the speed of train C be $x$ km/hr.
$\therefore$ Relative speed of B = $(100 - x )$ km/hr
$\therefore$ Time taken to cross = $\frac{\text{Length of both trains}}{\text{Relative speed}}$
⇒ $\frac{2}{60} = \frac{\frac{150+250}{1000}}{100-x}$
⇒ $\frac{1}{30} = \frac{2}{5(100-x)}$
⇒ 100 – $x$ = 12
$\therefore x$ = 88 km/hr
Hence, the correct answer is 88.
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