Book Fair Break-Even and Bulk Offer
The senior students of a school are running a three-day book fair to raise funds for the library. They have a fixed budget of Rs. 48,000. Venue hire is Rs. 9,000 for the three days, and insurance is Rs. 3,000. Each book costs Rs. 320 from the supplier and sells for Rs. 500. Unsold books can be returned to the supplier for Rs. 200 each. The team expects to sell between 150 and 220 books. A local shop offers to buy any unsold stock at Rs. 260 per book, but only if the team commits before the fair begins to supplying the shop with at least 40 books. The students must pay a 10% tax on profit, where profit is total revenue minus all costs, but only if profit exceeds Rs. 10,000. A volunteer calculates that buying 200 books will guarantee a profit of Rs. 26,000. The team must decide how many books to buy and whether to accept the shop's offer.
1. Calculate the number of books the team must sell to break even if it buys 200 books and does not accept the shop's offer. Show your working.
Read the worked answer
Fixed costs: Rs. 9,000 + Rs. 3,000 = Rs. 12,000. Cost of 200 books: 200 × Rs. 320 = Rs. 64,000. Total cost: Rs. 76,000. Let x be the number sold. Then 200 − x are unsold and returned for Rs. 200 each. Revenue: 500x + 200(200 − x) = 500x + 40,000 − 200x = 300x + 40,000. Set revenue equal to total cost: 300x + 40,000 = 76,000, so 300x = 36,000, and x = 120. Check: 120 sold gives Rs. 60,000; 80 returned gives Rs. 16,000; total Rs. 76,000. Break-even is 120 books.
2. Evaluate the volunteer's claim. If all 200 books sell, what is the correct net profit after tax? What error did the volunteer likely make?
Read the worked answer
If all 200 sell, revenue = 200 × 500 = Rs. 100,000. Total cost = 200 × 320 + 12,000 = Rs. 76,000. Profit before tax = Rs. 24,000. Since this exceeds Rs. 10,000, tax = 10% × 24,000 = Rs. 2,400. Net profit = Rs. 21,600. The claim of Rs. 26,000 is therefore too high by Rs. 4,400. A likely error is to ignore the 10% tax (which accounts for Rs. 2,400) and also undercount fixed costs by Rs. 2,000, or to use an incorrect margin. The claim is also not a guarantee, because sales may be below 200.
3. If the team buys 200 books and sales are 150, compare net profit with and without the shop's offer. Assume the shop takes exactly 40 unsold books and the remaining unsold books are returned to the supplier.
Read the worked answer
Without the offer: 150 sold for Rs. 500 = Rs. 75,000. 50 unsold returned at Rs. 200 = Rs. 10,000. Revenue = Rs. 85,000. Cost = Rs. 76,000. Profit = Rs. 9,000, which is below Rs. 10,000, so no tax. Net profit = Rs. 9,000. With the offer: 150 sold = Rs. 75,000. 40 unsold to the shop at Rs. 260 = Rs. 10,400. 10 remaining unsold returned at Rs. 200 = Rs. 2,000. Revenue = Rs. 87,400. Profit before tax = 87,400 − 76,000 = Rs. 11,400. Tax = 10% × 11,400 = Rs. 1,140. Net profit = Rs. 10,260. The offer improves net profit by Rs. 1,260 at this sales level, so it is worth accepting if the team is confident of selling at least 150.