Wholesale Exercise-Book Mixture with Damage and Discount
A stationer buys two grades of exercise books. Grade A costs ₹48 per dozen and Grade B costs ₹36 per dozen. He mixes 30 dozen of Grade A with 20 dozen of Grade B and marks the mixture at a price that would yield 25% profit if the entire 50 dozen were sold at the marked price. Before sale, 8% of the mixed stock is damaged by dampness and earns nothing. To clear the remaining stock, the stationer offers a flat 10% discount on the marked price. He claims that even after the damage and discount he is making a profit, and he wants to know the largest discount he could have offered on the marked price without incurring a loss on the whole transaction. Treat the cost of all 50 dozen as the base, ignore taxes, and assume the discount applies only to the sellable books.
1. Find the cost price per dozen of the mixture and the marked price per dozen.
Read the worked answer
Cost of 30 dozen Grade A = 30 × 48 = ₹1,440. Cost of 20 dozen Grade B = 20 × 36 = ₹720. Total cost = ₹2,160 for 50 dozen, so cost price per dozen = 2160/50 = ₹43.20.
For 25% profit on the whole stock, total marked price = 1.25 × 2160 = ₹2,700. Marked price per dozen = 2700/50 = ₹54.
2. Calculate the actual profit or loss percent after damage and the 10% discount, and state whether the stationer's claim is correct.
Read the worked answer
8% of 50 dozen = 4 dozen damaged, so sellable stock = 46 dozen.
Discount 10% on marked price: selling price per dozen = 0.90 × 54 = ₹48.60. Total selling price = 46 × 48.60 = ₹2,235.60.
Profit = 2235.60 − 2160 = ₹75.60. Profit percent on total cost = (75.60/2160) × 100 = 3.5%.
The claim is correct, but the margin is small: about 3.5%, not 25%.
3. Find the maximum percentage discount on the marked price that would allow the stationer to break even.
Read the worked answer
To break even, total selling price must equal ₹2,160 from 46 dozen. Required selling price per dozen = 2160/46 = ₹46.9565 approximately.
Maximum discount = marked price − required selling price = 54 − 46.9565 = ₹7.0435 per dozen.
Discount percent = (7.0435/54) × 100 ≈ 13.04%. So the maximum discount is about 13.0%, not 10%; 10% is safe but leaves only a small profit.