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Topic Content:
- Profit and Loss
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: Selling price is the price at which a good or service is sold.
Cost Price: 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 1.5.1:
A farmer buys an animal for ₦40 000 and sells it for ₦33 000. What is the percentage loss?
Solution
C.P. = ₦40 000
S.P. = ₦33 000
Loss = ₦40 000 – ₦33 000
= ₦7000
Percentage loss = \( \frac{Loss}{Cost \: Price}\scriptsize \: \times \: 100 \% \)
= \( \frac{7,000}{40,000}\scriptsize \: \times \: 100 \% \)
= \( \frac{7,\not{0}\not{0}\not{0}}{40,\not{0}\not{0}\not{0}}\scriptsize \: \times \: 100 \% \)
= \( \frac{7}{40}\scriptsize \: \times \: 100 \% \)
= \( \frac{700}{40}\% \)
= \( \frac{70\not{0}}{4\not{0}}\% \)
= \( \frac{70}{4}\scriptsize \% \\ = \frac{35}{2}\scriptsize \% \\ = \scriptsize 17 \frac{1}{2} \% \\ = \scriptsize 17.5 \% \)
Example 1.5.2:
Find (i) the profit or loss and (ii) the selling price, for these cost prices.
(a) ₦400, profit 20%
(b) ₦375, loss 8%
Solution
a (i) C.P. = ₦400
Percentage profit = 20%
Profit = 20% × ₦400
= \( \frac{20}{100} \scriptsize \: \times \: ₦400 = ₦80 \)
(ii) Profit = Selling price (S.P.) – Cost Price C.P
∴ S.P. = Profit + C.P
= ₦80 + ₦400
= ₦480
b (i) C.P. = ₦375
% loss = 8%
loss = 8% × ₦375
= \( \frac{8}{100}\scriptsize \: \times \: ₦375 = ₦30 \)
(ii) Loss = Cost Price (C.P.) – Selling Price (S.P.)
S.P = C.P – Loss
S.P. = ₦375 – ₦30
S.P. = ₦345
Example 1.5.3:
A trader makes a loss of 10% when he sells a watch for ₦15 300.
(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. = ₦15 300
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 × 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 = ₦17 000
(b) % profit = 6%
C.P. = ₦17 000
Profit = 6% × ₦17 000
Profit = \( \frac{6}{100}\scriptsize \: \times \: ₦17,000 \)
= ₦1 020
Selling price = C.P. + Profit
= ₦17 000 + ₦1 020
= ₦18 020
