Original values, profit and simple interest

(a) £$72$

1. $$600\times 0.03$$
2. $$18\times 4$$
3. Simple interest uses the original £600 each year.
4. 600 $\times$ 0.03 $\times$ 4 = £72 interest.

• P1 Establishing $600\times 0.03$ or an equivalent valid method.
• P1 Establishing $18\times 4$ or an equivalent valid method.
• A1 Correct answer: £$72$

(a) £360

1. Interest each year: $0.03 \times 2400 = £72$.
2. Over 5 years: $5 \times 72 = £360$.

• M1 Finding one year's interest, £72.
• A1 The correct answer, £360.

(b) $30\%$

1. Profit: $52 - 40 = £12$.
2. As a percentage of the cost price:
   $$\frac{12}{40} \times 100 = 30\%$$

• M1 Writing $\frac{12}{40}$.
• A1 The correct answer, $30\%$.

(a) £75

1. The final £90 is 120% of the original charge.
2. Original charge = 90 $\div$ 1.2 = £75.

• B1 Correct answer: £75

(a) £$120$

1. The selling price is 130% of the cost price.
   $$156/1.3$$
2. Therefore £$120$.

• P1 The selling price is 130% of the cost price.
• A1 Correct answer: £$120$

(b) £$24$

1. Subtract both the table cost and delivery from the income.
   $$156-120-12$$
2. Therefore £$24$.

• M1 Subtract both the table cost and delivery from the income.
• A1 Correct answer: £$24$

(a) £380

1. The sale price is $85\%$ of the original price.
2. $$0.85 \times \text{original} = 323 \Rightarrow \text{original} = 323 \div 0.85 = 380$$

• M1 Recognising that £323 is $85\%$ (writing $0.85$ or $\frac{323}{85}$).
• A1 The correct answer, £380.

(b) £800

1. £832 is $104\%$ of the old rent.
2. $$832 \div 1.04 = 800$$

• M1 Writing $832 \div 1.04$.
• A1 The correct answer, £800.

(a) £$72$

1. $$45+9$$
2. $$54/0.75$$
3. Undo the £9 reduction first: £45 + £9 = £54.
4. £54 is 75% of the original price.
5. Original price = £54 $\div$ 0.75 = £72.

• P1 Establishing $45+9$ or an equivalent valid method.
• P1 Establishing $54/0.75$ or an equivalent valid method.
• A1 Correct answer: £$72$

(a) $2\%$ profit

1. £72 is $120\%$ of the cost price.
   $$\text{cost} = 72 \div 1.2 = 60$$
2. Sale price:
   $$72 \times 0.85 = 61.20$$
3. Profit as a percentage of cost:
   $$\frac{61.20 - 60}{60} \times 100 = 2\%$$

• P1 Finding the cost price: $72 \div 1.2 = £60$.
• P1 Finding the sale price: $72 \times 0.85 = £61.20$.
• P1 Finding the profit £1.20 and dividing by the cost, £60.
• A1 The correct answer, $2\%$ profit.

(a) 100p/(100 + p)

1. Returning to the original requires (1 + p/100)(1 $-$ q/100) = 1.
2. So 1 $-$ q/100 = 100/(100 + p).
3. Hence q = 100p/(100 + p).

• B1 Correct answer: 100p/(100 + p)