Answer:
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%.
