correct answer is : c) 176 meters, 22 m/sec

Explanation

Let the length of the train is ‘l’ m.
And the speed of the train is ‘s’ m/sec.

In 1^st case,
When a train crosses a telegraph post then the distance covered by the train is the length (l) of the train.
Here, A telegraph post crosses by a train in 8 seconds.
\therefore Length of the train is: \left(s\ \times\ 8\right) = 8s meter. _{(here distance is the train ‘l’)}
\therefore l = 8s meter

In 2^nd case,
When a train crosses a bridge, it means the train covered its own length (l) and the bridge length, means sum of the train and bridge length.
Here, A bridge 264 meters long crosses by a train in 20 seconds.
\therefore Length of the train is:
=\ \left(l\ +\ 264\right) _{[sum of the train and bridge length]} —–(i)
And distance covered by train is
= \left(s\ \times\ 20\right) _{[distance = speed × time]} —–(ii)

Here from (i) and (ii) we get,
\left(l\ +\ 264\ =s\ \times\ 20\right) _{[ Length of the train = distance covered by train]}
\rightarrow\left(8s\ +\ 264\ =\ s\ \times\ 20\right) _{[put the value of ‘l’]}
\rightarrow8s\ +\ 264\ =\ 20s
\rightarrow\ 12s\ =\ 264
\rightarrow\ s\ =\ 264\ \div\ 12
\rightarrow\ s\ =\ 22
\therefore The speed of the train is = 22 m/sec
And the length of the train is = 8s meter
= (8\times\ 22) meters
= 176 meters.
Ans: The length of the train is 176 meters, and the speed of the train is 22 m/sec.