IPA IP 2025 Question 34
A question IPA Japan published in 令和7年度 ITパスポート試験 公開問題 問34, translated into English. ITPEC is based on the same exams.
When 5,000 units of a product were sold, the sales were 60 million yen and the profit was 4 million yen. When the variable cost per unit of the product is 7,000 yen, at least how many more units need to be sold to make the profit 10 million yen or more?
Explanation
1,200 more units — find the price and the fixed cost from the current result, then divide the extra profit needed by the contribution margin per unit.
- •Unit price: 60,000,000 ÷ 5,000 = 12,000 yen
- •Variable cost of 5,000 units: 7,000 × 5,000 = 35,000,000 yen
- •Fixed cost: sales − variable cost − profit = 60,000,000 − 35,000,000 − 4,000,000 = 21,000,000 yen
- •Contribution margin per unit: 12,000 − 7,000 = 5,000 yen
- •Extra profit needed: 10,000,000 − 4,000,000 = 6,000,000 yen
- •Extra units: 6,000,000 ÷ 5,000 = 1,200
Check: 6,200 units give 6,200 × 5,000 − 21,000,000 = 10,000,000 yen, exactly the target.
Answer (b)
Why not others:
- •(a) 500 — divides the extra 6 million yen by the unit price of 12,000 yen, as if the whole price were profit
- •(c) 6,200 — the total number of units to sell, not how many more than the 5,000 already sold
- •(d) 7,500 — divides by the average profit per unit (4 million ÷ 5,000 = 800 yen), which ignores that the fixed cost is already covered
Key rule: Once the fixed cost is covered, every extra unit adds its contribution margin (price − variable cost) to profit.
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This question comes from the past questions IPA Japan publishes, translated into English by ITPEC Practice. ITPEC Practice is an independent study tool and is not affiliated with IPA or ITPEC. See the original paper (PDF) or Report an issue.