Profit and loss

Profit and Loss

Profit: Profit is the amount gained when the selling price is higher than the buying price. The formula to calculate profit is: $\text{Profit} = \text{Selling Price} - \text{Cost Price}$

Loss: Loss is the amount lost when the selling price is lower than the buying price. The formula to calculate loss is: $\text{Loss} = \text{Cost Price} - \text{Selling Price}$

Percentage Profit: Percentage profit is the profit expressed as a percentage of the cost price. The formula to calculate percentage profit is: $\text{Percentage Profit} = \frac{\text{Profit} \times 100}{\text{Cost Price}}$

Percentage Loss: Percentage loss is the loss expressed as a percentage of the cost price. The formula to calculate percentage loss is: $\text{Percentage Loss} = \frac{\text{Loss} \times 100}{\text{Cost Price}}$

Example of Profit

If a book is bought for 50 shillings and sold for 70 shillings, the profit made is: $\text{Profit} = 70 - 50 = 20 \text{ shillings}$

Example of Loss

If a pencil is bought for 30 shillings and sold for 20 shillings, the loss made is: $\text{Loss} = 30 - 20 = 10 \text{ shillings}$

Percentage Profit

Percentage profit is the profit expressed as a percentage of the cost price. The formula is: $\text{Percentage Profit} = \frac{\text{Profit} \times 100}{\text{Cost Price}}$

Percentage Loss

Percentage loss is the loss expressed as a percentage of the cost price. The formula is: $\text{Percentage Loss} = \frac{\text{Loss} \times 100}{\text{Cost Price}}$

Example of Percentage Profit

If a product is bought for 100 shillings and sold for 150 shillings, the percentage profit is: $\text{Percentage Profit} = \frac{(150 - 100) \times 100}{100} = \frac{50 \times 100}{100} = 50\%$

Example of Percentage Loss

If a product is bought for 200 shillings and sold for 150 shillings, the percentage loss is: $\text{Percentage Loss} = \frac{(200 - 150) \times 100}{200} = \frac{50 \times 100}{200} = 25\%$

Example 1

A ration is bought for 24,000 shs and sold for 36,000 shs. Find:

1. The profit made.
2. The percentage profit.

Solution:

1. The profit made:

   • Buying price: 24,000/=
   • Selling price: 36,000/=
   • Profit: Selling price - Buying price
   • Profit = 36,000 - 24,000 = 12,000/=

2. The percentage profit:

   • Percentage profit: (Profit made × 100%) / Buying price
   • Percentage profit = (12,000 × 100%) / 24,000 = ½ × 100% = 50%

Example 2

A dealer paid 800,000/= for a machine and sold it the following year for 600,000/=. Find:

1. The loss made.
2. The percentage loss.

Solution:

1. The loss made:

   • Buying price: 800,000/=
   • Selling price: 600,000/=
   • Loss: Buying price - Selling price
   • Loss = 800,000 - 600,000 = 200,000/=

2. The percentage loss:

   • Percentage loss: (Loss made × 100%) / Buying price
   • Percentage loss = (200,000 × 100%) / 800,000 = ¼ × 100% = 25%

Example 3

A merchant bought a laptop for 45,000/= and sold it for 60,000/=. Find:

1. The profit made.
2. The percentage profit.

Solution:

1. The profit made:

   • Buying price: 45,000/=
   • Selling price: 60,000/=
   • Profit: Selling price - Buying price
   • Profit = 60,000 - 45,000 = 15,000/=

2. The percentage profit:

   • Percentage profit: (Profit made × 100%) / Buying price
   • Percentage profit = (15,000 × 100%) / 45,000 = ⅓ × 100% = 33.33%

Example 4

A car dealer bought a car for 1,500,000/= and sold it for 1,200,000/=. Find:

1. The loss made.
2. The percentage loss.

Solution:

1. The loss made:

   • Buying price: 1,500,000/=
   • Selling price: 1,200,000/=
   • Loss: Buying price - Selling price
   • Loss = 1,500,000 - 1,200,000 = 300,000/=

2. The percentage loss:

   • Percentage loss: (Loss made × 100%) / Buying price
   • Percentage loss = (300,000 × 100%) / 1,500,000 = ⅕ × 100% = 20%

Example 5

A trader bought a set of furniture for 50,000/= and sold it for 70,000/=. Find:

1. The profit made.
2. The percentage profit.

Solution:

1. The profit made:

   • Buying price: 50,000/=
   • Selling price: 70,000/=
   • Profit: Selling price - Buying price
   • Profit = 70,000 - 50,000 = 20,000/=

2. The percentage profit:

   • Percentage profit: (Profit made × 100%) / Buying price
   • Percentage profit = (20,000 × 100%) / 50,000 = 2/5 × 100% = 40%

Example 6

A wholesaler bought an item for 120,000/= and sold it for 100,000/=. Find:

1. The loss made.
2. The percentage loss.

Solution:

1. The loss made:

   • Buying price: 120,000/=
   • Selling price: 100,000/=
   • Loss: Buying price - Selling price
   • Loss = 120,000 - 100,000 = 20,000/=

2. The percentage loss:

   • Percentage loss: (Loss made × 100%) / Buying price
   • Percentage loss = (20,000 × 100%) / 120,000 = ⅙ × 100% = 16.67%