Question

A trader bought 12 shirts for $150 altogether. He sold 11 them for $20 each and one for $10.

Work out his overall percentage profit or loss.

Answer 1

Percentage Profit: 53.3%

Explanation:

General Outline

Definitions

1. Identify revenue
2. Identify cost
3. Find profit/loss
4. Find percentage profit/loss

Definitions

Before beginning, review some terminology definitions:

- Revenue - Revenue is the amount of money that is brought in from selling things. If you have a cash register (and if everyone pays cash), it is the amount of money that comes into the register (ignoring any that goes out)

- Cost - Cost is the amount of money that is spent to run the business (in this case, the money spent purchasing the items so that they can later be sold).

- Profit/loss - Profit/loss is the difference between the Revenue and the Cost. Which terms is used depends on which quantity was larger:

--- Profit - If more money was made in revenue than spent in costs.

--- Cost - If more money was spent in costs than made in revenue.

`\text{Profit or Loss}=|\text{Revenue}-\text{Cost}|`

- Percentage Profit/loss - A ratio formed between the Profit/Loss and the Cost.

`\text{Percentage Profit}=\frac{\text{Profit}}{\text{Cost}}`
`\text{Percentage Loss}=\frac{\text{Loss}}{\text{Cost}}`

Side note: Percentage Profit is effective to see how "productive" the business opportunity is. For instance, if you make $100 profit, and only have $1 cost, you have a 9900% percentage profit (which is amazing)! However, if you make $100 profit, but your cost was $10,000, you only have a 1% percentage profit, which is not so great. ... yes, still a profit, but it takes a lot of money to get started, to get that $100 profit.

Step 1: Identify Revenue

In this situation, the revenue is the money brought in. "He sold 11 them for $20 each and one for $10"

`11 \text{ shirts} * \frac {\$20}{\text{ shirt}}=\$220`

`1 \text{ shirt} * \frac {\$10}{\text{ shirt}}=\$10`

`\$220+\$10=\$230`

So, the Revenue is $230

Step 2: Identify Cost

In this situation, the cost is the money the trader spent to purchase the shirts in the first place so that he could later sell them. "A trader bought 12 shirts for $150 altogether."

So, the Cost is $150

Step 3: Find Profit/Loss

By inspection, we can see that the Revenue is more than the Cost, so the trader had a profit.

`\text{Profit}=|\text{Revenue}-\text{Cost}|\\\text{Profit}=|\$230-\$150|\\\text{Profit}=|\$80|\\\text{Profit}=\$80`

So, the Profit is $80

Step 4: Find Percentage Profit/Loss

Substituting the known values into the formula for percentage profit:

`\text{Percentage Profit}=\frac{\text{Profit}}{\text{Cost}}`

`\text{Percentage Profit}=(\$80)/(\$150)`

`\text{Percentage Profit}=0.5\bar{3}`

`\text{Percentage Profit}=53.33\%`

So, the Percentage Profit is 53.3%