#### Answer

The rate of profit based on the cost is 40%.

#### Work Step by Step

Let r represent the rate of profit.
We can use the following guideline to solve this problem:
Selling price = Cost + Profit
So:
44.80 = 32 + r $\times$ 32
44.80 = 32 + 32r
12.80 = 32r
Divide both sides by 32
0.4 = r
Multiply this amount by 100% to convert it into percent.
So, 0.4 $\times$ 100% = 40%
The rate of profit based on the cost is 40%.