correct answer is : a) 65 meters, 11 m/s.

Explanation

Lets the length of the train is ‘l’ meters and its speed is ‘s’ m/s.
When a train crosses a bridge, it means the total distance covered by the train is the sum of the length (l) of the train and the length of the bridge.

In 1^st case,
The time taken to cross the first bridge is 25 seconds.
The distance covered by train is: \left(210\ +\ l\right) _{[sum of the train and bridge length]}
\therefore The speed of the train is = \frac{210\ +\ l}{25} m/s [ speed = \frac{distance}{time} ] —- (i)

In 2^nd case,
The time taken to cross the second bridge is 17 seconds.
The distance covered by train is: \left(122\ +\ l\right) _{[sum of the train and bridge length]}
\therefore The speed of the train is = \frac{122\ +\ l}{17} m/s [ speed = \frac{distance}{time} ] —- (ii)

Here, from equation (i) and (ii) we get,
\frac{210\ +\ l}{25} = \frac{122\ +\ l}{17}
\rightarrow\ 17\left(210\ +\ l\right)\ =\ 25\left(122\ +\ l\right)
\rightarrow\ \left(3570\ +\ 17l\right)\ =\ \left(3050\ +\ 25l\right)
\rightarrow\ 17l\ -\ 25l\ =\ 3050\ – 3570
\rightarrow\ -\ 8l\ =\ -\ 520
\rightarrow\ l\ =\ \frac{-\ 520}{-\ 8}
\rightarrow\ l\ =\ 65 meters
\therefore length of the train is 65 meters.
And Speed of the train is:
\rightarrow\ \frac{210\ +\ 65}{25} m/s. _{[put the value of ‘l’ in (i) equation]}
\rightarrow\ \frac{275}{25} m/s
\rightarrow\ 11 meter/second.
Ans: Length of the train is 65 meters and speed of the train is 11 meter/second.