Profit

Profit occurs when the selling price is greater than the buying price.

$\text{Profit} = \text{Selling price} - \text{Buying price}$

Loss

Loss occurs when the selling price is less than the buying price.

$\text{Loss} = \text{Buying price} - \text{Selling price}$

An orange was bought at 150 shillings and sold at 200 shillings.

(a) What was the profit generated?

• Buying price = 150 shillings
• Selling price = 200 shillings
• Profit = Selling price − Buying price
• Profit = 200 − 150 = 50 shillings

(b) What was the percentage profit?

$\text{Percentage profit} = \frac{\text{Profit}}{\text{Buying price}} \times 100$ $\text{Percentage profit} = \frac{50}{150} \times 100 = \frac{1}{3} \times 100 = 33.3\%$

Juma bought a pair of shoes at 25,000 shillings and sold it at 16,000 shillings.

(a) What loss did Juma get?

• Buying price = 25,000 shillings
• Selling price = 16,000 shillings
• Loss = Buying price − Selling price
• Loss = 25,000 − 16,000 = 9,000 shillings

(b) What was the percentage loss?

$\text{Percentage loss} = \frac{\text{Loss}}{\text{Buying price}} \times 100$ $\text{Percentage loss} = \frac{9000}{25000} \times 100 = \frac{9}{25} \times 100 = 36\%$

The carpenter made a door at a cost of 250,000 shillings and sold it at a profit of 10%.

(a) What profit did the carpenter get?

$\text{Profit} = 10\% \times \text{Buying price}$ $\text{Profit} = \frac{10}{100} \times 250000 = 25,000 \text{ shillings}$

(b) How much money did the carpenter get in total?

$\text{Total money} = \text{Buying price} + \text{Profit}$ $\text{Total money} = 250000 + 25000 = 275,000 \text{ shillings}$

When we know the selling price and loss percentage, we can find the buying price.

If loss = 20% of buying price:

$\text{Loss} = 0.2 \times \text{Buying price}$

But: Loss = Buying price − Selling price

So: $0.2x = x - \text{Selling price}$

Then solve for $x$ (the buying price).

An invoice is a list of items bought or sold with their quantities and unit prices. The symbol @ means "for each."

Total cost = Quantity × Unit price

Worked Example 4: Preparing an Invoice

On 3rd December 2025, Aneth had 23,000 shillings to buy:

• 2 pairs of socks @ 1,200 shillings
• 10 small exercise books @ 600 shillings
• 15 pens @ 250 shillings
• 5 pencils @ 100 shillings
• 4 erasers @ 150 shillings

Prepare an invoice and find the balance.

Balance = Money given − Total spent

$\text{Balance} = 23000 - 13250 = 9,750 \text{ shillings}$

• Profit = Selling price − Buying price
• Loss = Buying price − Selling price
• Percentage profit = $\frac{\text{Profit}}{\text{Buying price}} \times 100$
• Percentage loss = $\frac{\text{Loss}}{\text{Buying price}} \times 100$
• Selling price with profit = Buying price + (Profit% × Buying price)
• Selling price with loss = Buying price − (Loss% × Buying price)

In Tanzania, market vendors and shopkeepers use these skills every day. For example, a mama lisuku at Mwanza market buys 100 bananas at 500 shillings each (total 50,000 shillings) and sells them at 700 shillings each. She calculates her profit to know if her business is growing. Understanding profit, loss, and how to prepare an invoice helps small business owners track their earnings, plan their spending, and make better decisions for their families.