Finding the rate of a tax or commission

In this lesson, we solve problems where we find the rate of a tax or commission. We are usually given the amount on which the tax or commission is calculated and the tax or commission itself. The rate of a tax or commission is usually a percent.

The ratio of the tax or commission to the given amount multiplied by 100 gives the rate of a tax or commission as a percent.

Formula

$$The \: rate \: of \: a \: tax \: or \: commission = \lgroup \frac{tax \: or \: commission}{original \: amount} \rgroup \times 100\%$$

The sales tax for an item was $24.50 and it cost $350 before tax. Find the sales tax rate. Write your answer as a percentage.

Solution

Step 1:

Price before tax = $350

Sales tax = $24.50

Step 2:

Rate of sales tax = $\frac{24.50}{350} = 0.07 = 7\%$

Find the sales tax rate if the sales tax on the purchase of a $300 DVD player was $19.50.

Solution

Step 1:

Price of DVD player = $300

Sales tax = $19.50

Step 2:

Rate of sales tax = $\frac{19.50}{300} = 6.5\%$

A book salesman is paid a commission of $840 when he sold $21,000 worth of books in a month. What was the rate of commission paid for that month?

Solution

Step 1:

Amount of sales = $21,000

Commission earned = $840

Step 2:

Rate of commission = $\frac{840}{21000} \times 100 = 4\%$