Indicies - Explanation, Examples and Laws of Indicies

 

            Profit, Loss, and Discount

Everyday transactions  from buying groceries to selling goods - involve the ideas of profit, loss, and discount. These concepts form the foundation of business mathematics and financial decision-making.

---

Basic Terms You Must Know

Before diving into formulas, let’s define key terms used in trading:

• Cost Price (C.P.): The price at which an article is bought.

• Selling Price (S.P.): The price at which the article is sold.

• Marked Price (M.P.): The price shown on the article before any discount.

• Discount: The reduction given on the marked price.

• Profit or Gain: When the selling price is greater than the cost price.

• Loss: When the selling price is less than the cost price.

---

Formulas

$$\text{Profit} = S.P. - C.P.$$
$$\text{Loss} = C.P. - S.P.$$
$$\text{Percentage Profit or Loss} = \frac{\text{Profit or Loss}}{\text{Cost Price}} \times 100\%$$
$$\text{Discount} = M.P. - S.P.$$
$$\text{Percentage Discount} = \frac{\text{Discount}}{M.P.} \times 100\%$$

---

Worked Examples

Example 1

A trader buys a bag for GHS 400 and sells it for GHS 500. Find his profit and percentage profit.

$$\text{Profit} = 500 - 400 = 100$$
$$\text{Percentage Profit}=\frac{100}{400}\times 100=25\mathrm{\%}\mathrm{<br>}\mathrm{<br>}\mathrm{<br>}$$

Profit = GHS 100, Percentage Profit = 25%

---

Example 2

A radio is sold for GHS 480 at a loss of 20%. Find the cost price.

$$\text{Loss} = 20\% \text{ of C.P.}$$
$$S.P. = C.P. - \text{Loss} = C.P. - 0.2C.P. = 0.8C.P.$$
$$480 = 0.8C.P.$$
$$C.P. = \frac{480}{0.8} = 600$$

Cost Price = GHS 600

---

Example 3

A man sells a book at GHS 150, making a profit of 25%. Find the cost price.

$$S.P. = C.P. + 25\% \text{ of C.P.} = 1.25C.P.$$
$$150 = 1.25C.P.$$
$$C.P. = \frac{150}{1.25} = 120$$

Cost Price = GHS 120

---

Example 4

A table is bought for GHS 800 and sold at a loss of 15%. Find the selling price.

$$\text{Loss} = 15\% \text{ of } 800 = \frac{15}{100} \times 800 = 120$$
$$S.P. = 800 - 120 = 680$$

Selling Price = GHS 680

---

Example 5

A trader bought an item for GHS 2,000 and sold it for GHS 2,300. Find his percentage gain.

$$\text{Profit} = 2300 - 2000 = 300$$
$$\text{Percentage Profit} = \frac{300}{2000} \times 100 = 15\%$$

Percentage Profit = 15%

---

Example 6

A shirt was marked at GHS 250 and sold for GHS 200. Find the discount and percentage discount.

$$\text{Discount} = 250 - 200 = 50$$
$$\text{Percentage Discount} = \frac{50}{250} \times 100 = 20\%$$

Discount = GHS 50, Percentage Discount = 20%

---

Example 7

A trader bought a phone for GHS 1,500 and spent GHS 300 on repairs. He sold it for GHS 2,100. Find his profit percentage.

$$\text{Effective Cost Price} = 1500 + 300 = 1800$$
$$\text{Profit} = 2100 - 1800 = 300$$
$$\text{Percentage Profit} = \frac{300}{1800} \times 100 = 16.67\%$$

Profit Percentage = 16.67%

---

Example 8

A man bought goods for GHS 2,000 and sold them at a loss of 10%. Find his selling price.

$$\text{Loss} = 10\% \text{ of } 2000 = 200$$
$$S.P. = 2000 - 200 = 1800$$

Selling Price = GHS 1,800

---

Example 9

A trader allows a 5% discount on goods marked at GHS 1,000 but still makes a profit of 25%. Find the cost price.

$$S.P. = 1000 - 5\% \text{ of } 1000 = 1000 - 50 = 950$$
$$\text{Profit} = 25\% \text{ of C.P.} \Rightarrow S.P. = 1.25C.P.$$
$$950 = 1.25C.P.$$
$$C.P. = \frac{950}{1.25} = 760$$

Cost Price = GHS 760

---

Example 10

A trader bought a shirt for GHS 300 and sold it at a discount of 10% on the marked price of GHS 400. Find his profit percentage.

$$S.P. = 400 - 10\% \text{ of } 400 = 400 - 40 = 360$$
$$\text{Profit} = 360 - 300 = 60$$
$$\text{Percentage Profit} = \frac{60}{300} \times 100 = 20\%$$

Profit Percentage = 20%

---

Note:

• A discount reduces the selling price, but a trader may still earn profit if the marked price is set high enough.

• Profit and loss always depend on the cost price, not on the marked price.

• Business owners often adjust the marked price to balance discounts and profits.

---

           Assignment 

Try these questions.

1. A trader bought an article for GHS 1,200 and sold it for GHS 1,500. Find his profit percentage.

2. A man sells a radio for GHS 960 at a loss of 20%. Find the cost price.

3. An article is marked GHS 400 and sold at a discount of 15%. Find the selling price and discount.

4. Find the loss percentage when an item bought for GHS 500 is sold for GHS 425.

5. A trader bought a TV for GHS 2,500 and spent GHS 200 on repairs. He sold it for GHS 3,000. Find his profit percentage.

6. A watch is sold for GHS 270 at a profit of 12½%. Find the cost price.

7. A dress marked at GHS 800 is sold at a discount of 10%, still giving a profit of 20%. Find the cost price.

8. A trader sells an article for GHS 540 after giving a 10% discount on the marked price. If he gains 8%, find the marked price and cost price.

9. A man bought 100 oranges for GHS 150. He sold each at GHS 2. Find his total profit and percentage profit.

10. An article costs GHS 1,000 and is sold at a loss of 5%. Find the selling price.