1. Meaning of hardness in terms of $CaCO_3$

   Hardness is often expressed as the equivalent concentration of $CaCO_3$.

   For this, we use: $\text{Hardness as } CaCO_3 = \text{Normality of hardness-producing salt} \times \text{equivalent weight of } CaCO_3$

2. Given concentration of $CaSO_4$

   $[CaSO_4] = 10^{-3}\,M$

   Since $CaSO_4$ gives one $Ca^{2+}$ ion per formula unit, its valency factor is $2$.

   Therefore, its normality is: $N = M \times 2 = 10^{-3} \times 2 = 2 \times 10^{-3}\,N$

3. Equivalent weight of $CaCO_3$

   Molar mass of $CaCO_3 = 100$ g/mol

   Since $CaCO_3$ also has valency factor $2$, $\text{Eq. wt. of } CaCO_3 = \frac{100}{2} = 50\,g/eq$

4. Convert to grams per litre as $CaCO_3$

   $\text{Hardness} = N \times \text{eq. wt.} = 2 \times 10^{-3} \times 50 = 0.1\,g/L$

   $0.1\,g/L = 100\,mg/L$

5. Convert mg/L to ppm

   For dilute aqueous solutions, $1\,mg/L \approx 1\,ppm$

   Hence, $100\,mg/L = 100\,ppm$

6. Option check

   • A: $90$ ppm $\rightarrow$ incorrect
   • B: $100$ ppm $\rightarrow$ correct
   • C: $50$ ppm $\rightarrow$ incorrect
   • D: $10$ ppm $\rightarrow$ incorrect

Therefore, the hardness of water sample is: $\boxed{100\,ppm}$