(a) A man earns N150,000 per annum and has a tax-free allowance of N40,000. He pays 25 kobo in the naira as tax on his taxable income. The problem asks how much money he has left after paying taxes. (b) A bookshop has 650 copies of a book marked at N75 to make a 30% profit. 300 copies were sold at a 5% discount, and the remaining copies were sold at N75. The problem asks to calculate the overall percentage profit the bookshop made.

1. Problem Description

(a) A man earns N150,000 per annum and has a tax-free allowance of N40,

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0. He pays 25 kobo in the naira as tax on his taxable income. The problem asks how much money he has left after paying taxes.

(b) A bookshop has 650 copies of a book marked at N75 to make a 30% profit. 300 copies were sold at a 5% discount, and the remaining copies were sold at N

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5. The problem asks to calculate the overall percentage profit the bookshop made.

2. Solution Steps

(a)

Step 1: Calculate the taxable income.

Taxable income = Total income - Tax-free allowance

Taxable income = $150000 - 40000 = 110000$

Step 2: Calculate the tax paid. The tax rate is 25 kobo per naira, which is equivalent to 0.25 naira per naira or 25%.

Tax paid = 25% of taxable income

Tax paid = $0.25 \times 110000 = 27500$

Step 3: Calculate the remaining income.

Remaining income = Total income - Tax paid

Remaining income = $150000 - 27500 = 122500$

(b)

Step 1: Determine the cost price per book.

Since the marked price of N75 represents a 30% profit, we can write:

Marked price = Cost price + 30% of Cost price

$75 = \text{Cost price} + 0.30 \times \text{Cost price}$

$75 = 1.30 \times \text{Cost price}$

Cost price $= \frac{75}{1.30} \approx 57.69$

Step 2: Calculate the revenue from the 300 copies sold at a 5% discount.

Discounted price = $75 - (0.05 \times 75) = 75 - 3.75 = 71.25$

Revenue from 300 copies = $300 \times 71.25 = 21375$

Step 3: Calculate the revenue from the remaining copies.

Remaining copies = $650 - 300 = 350$

Revenue from 350 copies = $350 \times 75 = 26250$

Step 4: Calculate the total revenue.

Total revenue = Revenue from discounted copies + Revenue from remaining copies

Total revenue = $21375 + 26250 = 47625$

Step 5: Calculate the total cost.

Total cost = Number of copies $\times$ Cost price per copy

Total cost = $650 \times 57.69 \approx 37498.5$

Step 6: Calculate the total profit.

Total profit = Total revenue - Total cost

Total profit = $47625 - 37498.5 = 10126.5$

Step 7: Calculate the percentage profit.

Percentage profit $= \frac{\text{Total profit}}{\text{Total cost}} \times 100$

Percentage profit $= \frac{10126.5}{37498.5} \times 100 \approx 27.00\%$

3. Final Answer

(a) The man has N122,500 left.

(b) The percentage profit the bookshop would make on the whole is approximately 27.00%.