A family spends on groceries, rent, and other expenses in the ratio 3 : 5 : 2. Next year, groceries are expected to rise by 8%, rent by 4%, and other expenses to fall by 10%. What will be the overall percentage change in total expenditure?

Correct Answer: 2.4% increase

Let's determine the overall percentage change in total expenditure step-by-step.

Step 1: Understand the initial ratio of expenses
The family spends on groceries, rent, and other expenses in the ratio $3:5:2$.

For convenience, let the initial expenditures be:

• Groceries = $300$

• Rent = $500$

• Other expenses = $200$

The total initial expenditure is:

$\text{Total Initial Expenditure}=300+500+200=1000$

Step 2: Calculate the changes in each expense category

1. Groceries increase by 8%:
$\text{Increase in Groceries}=8\%\text{of}300=\frac{8}{100}\times 300=24$

2. Rent increases by 4%:
$\text{Increase in Rent}=4\%\text{of}500=\frac{4}{100}\times 500=20$

3. Other expenses fall by 10%:
$\text{Decrease in Other Expenses}=10\%\text{of}200=\frac{10}{100}\times 200=20$

Step 3: Calculate the net change in total expenditure

$\text{Net Change}=+24+20-20=+24$

Since the net change is positive (+24), there is an increase in total expenditure.

Step 4: Calculate the overall percentage change

$\text{Overall Percentage Change}=\left(\frac{\text{Net Change}}{\text{Total Initial Expenditure}}\right)\times 100$

$\text{Overall Percentage Change}=\left(\frac{24}{1000}\right)\times 100=2.4\%$

Therefore, the overall percentage change in total expenditure is a 2.4% increase.