For a uniform spring, the force constant is inversely proportional to length: $k\ell =$ constant.

If the original length is $L$ with $k=15$ N/m, and the pieces are in ratio $1:3$, the smaller piece has length $L/4$.

$k_{\text{small}}\cdot \frac{L}{4}=15\cdot L\Rightarrow k_{\text{small}}=60$ N/m.