20 " mL of " x M HCl neutralises completely 10 " mL of " 0.1 M `NaHCO_3` solution and a further 5 " mL of " 0.2 M `Na_2CO_3` to methyl orange end point. What is the value of `x`?

Explanation

To find the value of \( x \) in the question, we will use the concept of milliequivalents and the neutralization reaction between HCl and the sodium bicarbonate (NaHCO₃) and sodium carbonate (Na₂CO₃) solutions.

### Step-by-Step Solution:

1. **Identify the neutralization reaction:**
- HCl neutralizes NaHCO₃ and Na₂CO₃. The neutralization reactions are:
- \( \text{HCl} + \text{NaHCO}_3 \rightarrow \text{NaCl} + \text{H}_2\text{O} + \text{CO}_2 \)
- \( \text{2 HCl} + \text{Na}_2\text{CO}_3 \rightarrow 2 \text{NaCl} + \text{H}_2\text{O} + \text{CO}_2 \)
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