Calculating Expenditure Percentage Increase

This problem involves calculating the change in expenditure based on changes in income and savings. We know that Income = Savings + Expenditure. The key is that the savings amount stays constant even when the income increases.

Step-by-Step Solution

1. Assume an Initial Income: Let the initial income be $100$. This simplifies percentage calculations.

   • Initial Income = $100

2. Calculate Initial Savings and Expenditure: Amina saves 16% of her income.

   • Initial Savings = $16\% \times 100 = 16$
   • Initial Expenditure = Initial Income - Initial Savings = $100 - 16 = 84$

3. Calculate New Income: Her income increases by 20%.

   • Increase in Income = $20\% \times 100 = 20$
   • New Income = $100 + 20 = 120$

4. Calculate New Expenditure: Her savings amount remains the same ($16$).

   • Savings = $16$
   • New Expenditure = New Income - Savings = $120 - 16 = 104$

5. Calculate Percentage Increase in Expenditure:

   • Amount of Increase in Expenditure = New Expenditure - Initial Expenditure = $104 - 84 = 20$
   • Percentage Increase = $\frac{\text{Increase in Expenditure}}{\text{Initial Expenditure}} \times 100$
   • Percentage Increase = $\frac{20}{84} \times 100$
   • Percentage Increase = $\frac{5}{21} \times 100 \approx 23.8095\%$

   Rounding to one decimal place, the percentage increase in expenditure is $23.8\%$.