A toy train crosses 210m and 122m long tunnels in 25 and 17 seconds respectively with the same speed. The length of the train is ……

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.

Correct option is B) 65 m