I) The number of moles of acid in the average titre.

$$\text{Moles of acid A} = \text{Concentration of A} \times V_A$$ $$\text{Moles of acid A} = 0.10 \text{ mol dm}^{-3} \times 0.00710 \text{ dm}^3 = 0.000710 \text{ mol}$$

The number of moles of acid in the average titre is $\boxed{\text{0.000710 mol}}$.

$$\text{Concentration of B} = \frac{\text{Mass of Na}_2\text{CO}_3 \text{ per dm}^3}{\text{Molar mass of Na}_2\text{CO}_3}$$ $$\text{Concentration of B} = \frac{1.325 \text{ g/dm}^3}{106 \text{ g/mol}} = 0.0125 \text{ mol dm}^{-3}$$

$$\text{Moles of Na}_2\text{CO}_3 = \text{Concentration of B} \times V_B$$ $$\text{Moles of Na}_2\text{CO}_3 = 0.0125 \text{ mol dm}^{-3} \times 0.025 \text{ dm}^3 = 0.0003125 \text{ mol}$$

The number of moles of sodium trioxocarbonate (IV) in the volume of B pipette is $\boxed{\text{0.0003125 mol}}$.

$$\text{Mole ratio (Acid : Base)} = \text{Moles of acid A} : \text{Moles of Na}_2\text{CO}_3$$ $$\text{Mole ratio} = 0.000710 \text{ mol} : 0.0003125 \text{ mol}$$

To simplify the ratio, divide both sides by the smaller value (0.0003125):

$$\frac{0.000710}{0.0003125} : \frac{0.0003125}{0.0003125}$$ $$2.272 : 1$$

This ratio is approximately $2:1$.

The base is sodium trioxocarbonate (IV) ($\text{Na}_2\text{CO}_3$).
A $2:1$ mole ratio of acid to base suggests that the acid is monoprotic (has one acidic hydrogen) and reacts with the carbonate, which is a diprotic base (can accept two protons).
The teacher's hint suggests $\text{HCl}$. Hydrochloric acid ($\text{HCl}$) is a monoprotic mineral acid.
The reaction between $\text{HCl}$ and $\text{Na}_2\text{CO}_3$ is:

$$2\text{HCl(aq)} + \text{Na}_2\text{CO}_3\text{(aq)} \rightarrow 2\text{NaCl(aq)} + \text{H}_2\text{O(l)} + \text{CO}_2\text{(g)}$$

This equation shows that 2 moles of $\text{HCl}$ react with 1 mole of $\text{Na}_2\text{CO}_3$, which matches our calculated mole ratio of approximately $2:1$.

Therefore, the mole ratio of acid to base is approximately $\boxed{2:1}$.
The acid in (a) could be hydrochloric acid ($\text{HCl}$).
Reason: The calculated mole ratio of acid to base is approximately $2:1$, which is consistent with a monoprotic acid like $\text{HCl}$ reacting with a diprotic base like $\text{Na}_2\text{CO}_3$.