Given data

• Nitric acid solution is $75\%$ by mass.
• Density of solution $= 1.25\ \text{g mL}^{-1}$.
• Mass of pure $\mathrm{HNO_3}$ required $= 30\ \text{g}$.

Use mass percentage relation

Since the solution is $75\%$ by mass, $\frac{\text{mass of solute}}{\text{mass of solution}} \times 100 = 75$

Let mass of solution required be $m$ g. Then, $\frac{30}{m} \times 100 = 75$

$\frac{30}{m} = 0.75$

$m = \frac{30}{0.75} = 40\ \text{g}$

Convert mass of solution to volume using density $\text{Density} = \frac{\text{mass}}{\text{volume}}$

$\text{Volume} = \frac{\text{mass}}{\text{density}} = \frac{40}{1.25} = 32\ \text{mL}$

Final answer The required volume of nitric acid solution is $\boxed{32\ \text{mL}}$

Option check

• A: $32$ ✅
• B: $40$ ❌
• C: $55$ ❌
• D: $45$ ❌