A) 100 m
B) 120 m
C) 140 m
D) 160 m
Correct Answer: A
Solution :
Let die speed of a train be x m/s and length be y m. 1st condition, when \[t=8\,s\] \[\text{Time=}\frac{\text{Distance}}{\text{Speed}}\] \[\Rightarrow \] \[\text{8=}\frac{y}{x}\] \[\Rightarrow \] \[y=8x\] ...(i) IInd condition, When \[t=24\,s,\] speed \[=x\] Relative distance \[=y+200\] \[\because \] \[\text{Time=}\frac{\text{Relative distance}}{\text{Speed}}\] \[\therefore \] \[24=\frac{y+200}{x}\] \[\Rightarrow \] \[24x=y+200\] \[\Rightarrow \] \[24x=8x+200\] [from Eq. (i)] \[\Rightarrow \] \[16x=200\] \[\Rightarrow \] \[x=\frac{25}{2}\] \[\therefore \] \[x=\frac{25}{2}\] \[\therefore \] from Eq. (i) \[y=8x=8\times \frac{25}{2}=100\]
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