Assume Initial Income

Let the initial monthly income of the person be $100$.

$\text{Income} = 100$

Calculate Initial Savings and Expenditure

Since the person saves $30\%$ of his income, initial savings = $30$. Therefore, initial expenditure = $\text{Income} - \text{Savings} = 100 - 30 = 70$.

$\text{Savings}_1 = 30, \quad \text{Expenditure}_1 = 70$

Calculate New Income and New Savings

The monthly income increases by $20\%$, so new income = $100 + 20 = 120$. The savings increases by $20\%$ of the previous savings ($30$), so new savings = $30 \times 1.20 = 36$.

$\text{Income}_2 = 120, \quad \text{Savings}_2 = 36$

Calculate New Expenditure

New expenditure is the difference between new income and new savings: $\text{Expenditure}_2 = 120 - 36 = 84$.

$\text{Expenditure}_2 = 84$

Calculate Percentage Increase in Expenditure

The increase in expenditure is $84 - 70 = 14$. The percentage increase is calculated with respect to the initial expenditure ($70$).

$\text{Percentage Increase} = \frac{84 - 70}{70} \times 100 = \frac{14}{70} \times 100 = 20\%$