Let's break down the problem step by step to calculate Josh's percentage profit.
Step 1: Calculate the total cost of buying the books:
Josh buys 120 books, each for £4.
Total cost = Number of books × Cost per book
Total cost = 120 × £4 = £480
Step 2: Calculate the number of books sold in each category:
- Half of the books are sold for £5 each.
- 40% of the books are sold for £7 each.
- The remaining books are sold for £8 each.
Books sold for £5:
Number of books = 120 / 2 = 60 books
Books sold for £7:
Number of books = 40% of 120 = 0.4 × 120 = 48 books
Books sold for £8:
Number of books = Total books - (Books sold for £5 + Books sold for £7)
Number of books = 120 - (60 + 48) = 120 - 108 = 12 books
Step 3: Calculate the total revenue from selling the books:
Revenue from books sold for £5:
Revenue = Number of books × Sell price per book
Revenue = 60 × £5 = £300
Revenue from books sold for £7:
Revenue = Number of books × Sell price per book
Revenue = 48 × £7 = £336
Revenue from books sold for £8:
Revenue = Number of books × Sell price per book
Revenue = 12 × £8 = £96
Total revenue:
Total revenue = Revenue from £5 books + Revenue from £7 books + Revenue from £8 books
Total revenue = £300 + £336 + £96 = £732
Step 4: Calculate the profit:
Profit = Total revenue - Total cost
Profit = £732 - £480 = £252
Step 5: Calculate the percentage profit:
Percentage profit = (Profit / Total cost) × 100%
Percentage profit = (£252 / £480) × 100% = 52.5%
So, Josh's percentage profit is 52.5%.
