Question

A bookshop had 650 copies of a book for sale. The books were marked at 75 per copy in order to make a profit of 30%. A bookseller bought 300 copies at 5% discount. If the remaining copies sold at 75 each, calculate the percentage profit of the bookshop will make on the whole

Answer 1

The bookshop will make a percentage profit of 23.83% on the whole.

Step-by-step explanation:

To calculate the percentage profit of the bookshop on the whole, we need to consider the cost price and selling price of all the copies of the book.

The selling price of each book is $75.

The bookshop initially had 650 copies of the book marked at $75 each, with the aim of making a profit of 30%.

To calculate the cost price of each book, we can use the formula:

Cost price = Selling price / (1 + Profit percentage)

So, the cost price of each book is $75 / (1 + 0.3) = $57.69.

The bookshop sold 300 copies to a bookseller at a 5% discount, which means the discounted cost price of each book is $57.69 - ($57.69 * 0.05) = $54.81.

The bookshop then sold the remaining copies at $75 each.

To calculate the overall profit made by the bookshop, we need to find the total cost price and total selling price.

Total cost price = (300 * $54.81) + (350 * $57.69) = $19,166.50 + $20,195.50 = $39,362.

Total selling price = (300 * $75) + (350 * $75) = $22,500 + $26,250 = $48,750.

The overall profit made by the bookshop is the difference between the total selling price and the total cost price.

Profit = Total selling price - Total cost price = $48,750 - $39,362 = $9,388.

The percentage profit can be calculated using the formula:

Percentage profit = (Profit / Total cost price) * 100

Percentage profit = ($9,388 / $39,362) * 100 = 23.83%.

Answer 2

The percentage profit of the bookshop will make on the whole is 27%.

Step-by-step explanation:

The following are given in the question:

Copies of books for sale = 650

Selling price per copy = 75

Copies sold at 5% discount = 300

Discount rate = 5%, or 0.05

Percentage profit per copy = 30%, or 0.30

To calculate cost per copy, the following formula is used:

Percentage profit per copy = (Selling price per copy – Cost per copy) / Cost per copy …….. (1)

Substituting the values into equation (1) and solve for Cost per copy, we have:

30% = (75 - Cost per copy) / Cost per copy

0.30 * Cost per copy = 75 - Cost per copy

(0.30 * Cost per copy) + Cost per copy = 75

1.30 * Cost per copy = 75

Cost per copy = 75 / 1.30

Cost per copy = 57.6923076923077

Therefore, we have:

Total cost = Copies of books for sale * Cost per copy = 650 * 57.6923076923077 = 37,500

Selling price at 5% discount = 75 * (100% - Discount rate) = 75 * (100% - 5%) = 75 * 95% = 71.25

Revenue from sales at selling price at 5% discount = Selling price at 5% discount * Number of sales at 5% discount = 71.25 * 300 = 21,375

Revenue from the remaining copies sold at 75 per copy = (Copies of books for sale - 300) * 75 = (650 - 300) * 75 = 350 * 75 = 26,250

Total revenue = Revenue from sales at selling price at 5% discount + Revenue from sales at 75 per copy = 21,375 + 26,250 = 47,625

Total profit = Total revenue - Total cost = 47,625 - 37,500 = 10,125

To calculate the percentage profit of the bookshop will make on the whole, the following formula is used:

Percentage profit on the whole = (Total profit / Total cost) * 100 ................ (2)

Substituting the relevant values form above into equation (2), we have:

Percentage profit on the whole = (10,125 / 37,500) * 100

Percentage profit on the whole = 0.27 * 100

Percentage profit on the whole = 27%

Therefore, the percentage profit of the bookshop will make on the whole is 27%.