Question

The expenditure of a household on food, clothing, and entertainment is in the ratio 2: 4: 4. In the coming year, the cost of food is expected to fall by 10%, clothing to rise by 5%, and entertainment to fall by 15%. What is the percent change (increase or decrease) in the total household expenditure?

• A. 5% decrease
• B. 6% increase
• C. 6% decrease
• D. 5% increase

Answer 1

Answer:

C. 6% decrease

Let the original expenditures be:

• Food = (2x)

• Clothing = (4x)

• Entertainment = (4x)

Total original expenditure:

2x+4x+4x=10x

Now apply the changes:

Food

10% decrease:

$2x \times \frac{90}{100}=1.8x$

Clothing

5% increase:

$4x \times \frac{105}{100}=4.2x$

Entertainment

15% decrease:

$4x \times \frac{85}{100}=3.4x$

New total expenditure:

$1.8x+4.2x+3.4x=9.4x$

Change in expenditure:

$10x-9.4x=0.6x$

Percentage change:

$\frac{0.6x}{10x}\times100=6\%$

Therefore, the total household expenditure decreases by:

$\boxed{6\% \text{ decrease}}$