Sum of squares of first n natural numbers = $\dfrac{n × (n + 1) (2n + 1)}{6}$
Squares of sum of first n natural numbers = $\dfrac{n × (n + 1)}{2} × \dfrac{n × (n + 1)}{2}$
Now the ratio is $\dfrac{n × (n + 1) (2n + 1)}{6}$ : $\dfrac{n × (n + 1)}{2} × \dfrac{n × (n + 1)}{2}$
Plug in the values of each option and check the ratio.
(a) n = 15; (15 × 16 × 31)/6 : (15 × 16 × 15 × 16)/4 = 40 × 31 : 120 × 120 which not in the ratio of 17 : 325. [Eliminate]
(b) n = 25; (25 × 26 × 51)/6 : (25 × 26 × 25 × 26)/4 = 25 × 13 × 17 : 325 × 325 which is in the ratio 17 : 325 [ = Answer]
No need to check for the remaining options after this.