Apple Trader: Two Selling Plans and a Target Price
A fruit trader buys 500 kg of apples at ₹40 per kg and spends nothing else initially. In transit, 8% of the apples spoil and cannot be sold. The trader sells 300 kg of the remaining good apples at ₹60 per kg. The rest of the good apples are sold later at ₹30 per kg. The trader is considering a second plan: sell all the good apples at a uniform ₹48 per kg. Storage for the later sale costs ₹800, and this cost applies only to the first plan; the uniform plan avoids it. The trader also wants to know the minimum uniform price per kg that would give an overall profit of 15% on the original cost. All quantities and rates are exact, and no other costs apply. The trader must choose a plan before the apples deteriorate further, so the decision cannot wait for a better price later.
1. Compute the overall profit or loss percentage under the first plan, including the storage cost.
Read the worked answer
Original cost = 500 × ₹40 = ₹20,000.
Spoilage = 8% of 500 = 40 kg, so good apples = 500 − 40 = 460 kg.
First plan revenue:
- 300 kg at ₹60 = ₹18,000
- Remaining 460 − 300 = 160 kg at ₹30 = ₹4,800
- Gross revenue = ₹18,000 + ₹4,800 = ₹22,800
Storage cost = ₹800, so net revenue = ₹22,800 − ₹800 = ₹22,000.
Profit = ₹22,000 − ₹20,000 = ₹2,000.
Profit percentage = (2,000 ÷ 20,000) × 100 = 10%.
2. Compute the profit percentage under the second plan and decide which plan is better on profit alone. How large is the difference?
Read the worked answer
Second plan revenue = 460 kg × ₹48 = ₹22,080. There is no storage cost.
Profit = ₹22,080 − ₹20,000 = ₹2,080.
Profit percentage = (2,080 ÷ 20,000) × 100 = 10.4%.
The second plan is better by ₹2,080 − ₹2,000 = ₹80, or 0.4 percentage points. The difference is small, but the uniform plan also avoids the risk of holding 160 kg in storage and depending on a later sale at ₹30 per kg. If the later price fell or storage costs rose, the gap would widen in favour of the uniform plan.
3. What minimum uniform price per kg is needed in the second plan to earn a 15% profit on the original cost? Compare this with the proposed ₹48 price.
Read the worked answer
Required profit = 15% of ₹20,000 = ₹3,000.
Required revenue = cost + profit = ₹20,000 + ₹3,000 = ₹23,000.
Good apples available = 460 kg, so required price = ₹23,000 ÷ 460 = ₹50 per kg.
At the proposed ₹48 per kg, revenue is ₹22,080, giving a profit of ₹2,080, which is only 10.4%, not 15%. The trader would need at least ₹50 per kg to reach the 15% target. The shortfall at ₹48 is ₹23,000 − ₹22,080 = ₹920, or ₹2 per kg over 460 kg. The trader should not describe ₹48 as meeting the 15% target.