The RELATION between Distance travelled, Speed of travel and the Time taken to travel this distance is given by:

Distance = Speed × Time---- (A)

$(? Time = \;\frac{{Distance}}{{Speed}}\;)$---- (B)

Let the LENGTH of the train be 'L' metres.

According to the given information the train crosses the 120 metre platform in 'T' seconds.

Using above formulae:

Time taken to cross the platform = (TOTAL Distance covered)/Speed

$(\therefore {\rm{\;T\;}} = \frac{{L + 120}}{{Speed}}\;)$---- (1)

Consider Statement (I), according to which the train crosses a signal post in 'R' seconds

Using above formulae:

Time taken to cross the signal post = (Total Distance covered)/Speed

$(\therefore {\rm{R\;}} = \frac{L}{{Speed}})$---- (2)

The values of 'T' and 'R' are given values, so the only variables we need to solve for are 'L' and Speed.

We have 2 equations to solve for 2 variables.

∴ Statement (I) is ENOUGH to find the length of the train.

Now consider Statement (II),according to whichthe train moves at 90 km/hr.

$(\therefore {\rm{Speed\;}} = {\rm{\;}}90\frac{{{\rm{km}}}}{{{\rm{hr}}}} = 90 \times \frac{5}{{18}}{\rm{m}}/{\rm{s\;}} = {\rm{\;}}25{\rm{\;m}}/{\rm{s}})$

Substituting this value in equation (1) we can get the length of the train.

∴ Statement (II) alone can give the length of the train.

∴ Both statements are individually sufficient to find the answer