A) 28 km/h
B) 27 km/h
C) 25 km/h
D) 24 km/h
Correct Answer: C
Solution :
Let the speed of train be x km/h and its length be y h When the train crosses a man, it covers its own length According to the question, \[\frac{y}{(x-3)\times \begin{matrix} 5 \\ 18 \\ \end{matrix}}=10\] \[\Rightarrow \] \[18y=10\times 5(x-3)\] \[\Rightarrow \] \[18y=50x-150\] ? (i) And, \[\frac{y}{(x-5)\times \begin{matrix} 5 \\ 18 \\ \end{matrix}}=11\] \[\Rightarrow \] \[18y=55y(x-5)\] \[\Rightarrow \] \[18y=55y-275\] ? (ii) From Eqs., (i) and (ii), \[55x-275=50x-150\] \[\Rightarrow \] \[55x-50x=275-150\] \[\Rightarrow \] \[5x=125\] \[\Rightarrow \] \[x=\frac{125}{5}=25\] \[\therefore \] Speed of the train \[=25\,\text{km/h}\]
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