Question

Kory pays 1/3 of his income in tax. He then spend 4/5 of what remains after tax, and places the rest into a savings account. What fraction of his income does he put into his saving account?

Answer 1

2/5 of income put into savings

Explanation:

Let Kory's income be X

1/3 of his income goes to taxes so taxes are X/3

Remaining is (1- 2/3) of income = (2/3 ) X

He spends 4/5 of this remaining amount

So balance after expenditure = (1- 4/5) = 1/5 of the remaining income and this amount is put into savings

Fraction of income in savings = 1/5 x 2/3 X = (2/15)X

So fraction put into savings account is 1/5 of total income

If you find it confusing to work with fractions such as these, I suggest an alternate approach which may make it easier to understand

Pick an amount for total income. Since the denominators are 3 and 5, choose an amount which is divisible by both 3 and 5 or in other words divisible by 15

Let's choose 300, a convenient number

Tax Paid = 1/3 x 300 = 100

Income after tax = 300 - 100 = 200
which is same as 2/3 x 300

Spending = 4/5 x 200 = 160

Balance in savings = 200 - 160 = 40 same as 1/5 x 200

So amount in savings as a fraction of income = 40/300 = 2/15