Question

A family paid 12 percent of its annual after tax income on food last year. This amount was equal to 10 percent of its annual before tax income last year. Which of the following is closest to the percent of the family's annual before-tax income that was paid for tares last year? a. 8% b. 12% c. 17% d. 20%e. 25%

Answer 1

Option c. 17%

Explanation:

Data provided in the question:

Amount paid on food last year = 12% of Annual after tax income

Amount paid on food for the current year = 10% of Annual before tax income

Now,

Let the after tax income be 'x'

and tax be 'y'

Therefore,

Income before tax = x + y

Amount paid on food = 12% of x

According to the question

12% of x = 10% of (x + y)

or

0.12x = 0.10 (x + y)

or

1.2x - x = y

0.2x = y

or

x = 5y

Thus,

percent of the family's annual before-tax income that was paid for tares last year

= [Tax ÷ Income before tax] × 100%

= [ y ÷ ( x + y )] × 100%

= [ y ÷ ( 5y + y )] × 100%

or

= 0.167 × 100% ≈ 17%

Hence,

Option c. 17%