Lesson 1, Topic 4
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# Commercial Transactions

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### Profit and Loss

1. Profit = Selling price (S.P.) – Cost Price C.P

2. Loss = Cost Price (C.P.) – Selling Price  (S.P.)

Where

Selling price: is the price at which a good or service is sold.

Cost Price: Is the price at which a good is bought.

When S.P. > C.P., a profit is made

When C.P. > S.P., a loss is made

3. Percentage profit = $$\frac{Profit}{Cost \: Price}\scriptsize \: \times \: 100 \%$$

4. Percentage loss = $$\frac{Loss}{Cost \: Price}\scriptsize \: \times \: 100 \%$$

5. Profit = Percentage $$\scriptsize \: \times \:$$ Cost price

### Example 1

A farmer buys an animal for N40 000 and sells it for N33 000. What is the percentage loss?

Solution

C.P. = N40 000

S.P. = N33 000

Loss = N40 000 – N33 000

= N7000

Percentage loss = $$\frac{Loss}{Cost \: Price}\scriptsize \: \times \: 100 \%$$

= $$\frac{7,000}{40,000}\scriptsize \: \times \: 100 \%$$

= $$\frac{70}{4}\scriptsize \% \\ = \frac{35}{2}\scriptsize \% \\ = \scriptsize 17 \frac{1}{2} \% \\ = \scriptsize 17.5 \%$$

### Example 2

Find (i) the profit or loss and (ii) the selling price, for these cost prices.

(a) N400, profit 20%

(b) N375, loss 8%

Solution

a(i)   C.P. = 400

Percentage profit = 20%

Profit = 20% x N400

= $$\frac{20}{100} \scriptsize \: \times \: N400 = N80$$

(ii) Profit = Selling price (S.P.) – Cost Price C.P

S.P. = Profit + C.P

= N80 + N400

= N480

b(i) C.P. = N375

% loss = 8%

loss = 8%  x N375

= $$\frac{8}{100}\scriptsize \: \times \: N375 = N30$$

(ii) Loss = Cost Price (C.P.) – Selling Price  (S.P.)

S.P = C.P – Loss

S.P. = N375  – N30

S.P. = N345

### Example 3

A trader makes a loss of 10% when he sells a watch for N15 300.

(a) What did it cost?

(b) Find out how much he should have sold it for to make a profit of 60%

Solution

(a) % loss = 10%

S. P. = N15 300

But, loss  = C.P. – S.P.

% loss = $$\frac{Loss}{Cost \: Price}\scriptsize \: \times \: 100 \%$$

10 = $$\frac{C.P \: -\: S.P}{C.P}\scriptsize \: \times \: 100 \%$$

$$\frac{10}{1} = \frac{C.P \: -\: 15,300}{C.P}\scriptsize \: \times \: 100 \%$$

$$\frac{10}{1} = \frac{100(C.P \: -\: 15,300)}{C.P}$$

Cross multiply

10   x C.P. = 100 (C.P. – 15 300)

10 C.P. = 100 C.P. – 1,530,000

Collect like terms

1 530 000 = 100 C.P. – 10 C.P.

1 530 000 = 90 C.P.

90 C.P. = 1 530 000

Divide both sides by 90

$$\frac{90 C.P}{90} = \frac{1530000}{90}$$

:-Cost price = N17 000

(b) % profit = 6%

C.P. =  N17 000

Profit = 6% x N17 000

Profit = $$\frac{6}{100}\scriptsize \: \times \: N17,000$$

= N1 020

Selling price = C.P.  + Profit

= N17 000 + N1020

= N18 020

#### Responses

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