Correct option is (B) 65 m
Let the length of the toy train be x m.
Given that length of tunnel I is 210 m and
length of tunnel II is 122 m
Since, train crosses the tunnels.
So, train have to cover distance (210 + x) m to cross train I and cover distance (122 + x) m to cross train II.
Speed of toy train while crossing tunnel I \(=\frac{\text{Covered distance}}{\text{Taken time}}\)
\(=\frac{(210+x)}{25}\,m/s\) ___________(1)
Speed of toy train while crossing tunnel II \(=\frac{\text{Covered distance}}{\text{Taken time}}\)
\(=\frac{(122+x)}{17}\,m/s\) ___________(2)
Since, speed of train is same while crossing both tunnels.
\(\therefore\) \(\frac{210+x}{25}=\frac{122+x}{17}\)
\(\Rightarrow\) 17 (210+x) = 25 (122+x)
\(\Rightarrow\) 3570 + 17x = 3050 + 25x
\(\Rightarrow\) 25x - 17x = 3570 - 3050
\(\Rightarrow\) 8x = 520
\(\Rightarrow\) x = \(\frac{520}8\) = 65
Hence, the length of the train is 65 m.
