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JSS2: MATHEMATICS - 3RD TERM

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  1. Expansion and Factorization of Algebraic Expressions | Week 1
    4Topics
    |
    1 Quiz
  2. Algebraic Expansion and Factorization of Algebraic Expression | Week 2
    4Topics
    |
    1 Quiz
  3. Algebraic Fractions I | Week 3
    4Topics
    |
    1 Quiz
  4. Addition and Subtraction of Algebraic Fractions | Week 4
    2Topics
    |
    1 Quiz
  5. Solving Simple Equations | Week 5
    4Topics
    |
    1 Quiz
  6. Linear Inequalities I | Week 6
    4Topics
    |
    1 Quiz
  7. Linear Inequalities II | Week 7
    2Topics
    |
    1 Quiz
  8. Transactions in the Homes and Offices | Week 8
    5Topics
    |
    1 Quiz
  9. Quadrilaterals | Week 9
    2Topics
    |
    1 Quiz
  10. Angles in a Polygon | Week 10
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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 + N40 

= 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 

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