IPA IP 2023 Question 13
A question IPA Japan published in 令和5年度 ITパスポート試験 公開問題 問13, translated into English. ITPEC is based on the same exams.
Same question on ITPEC: Oct 2025 Q72
The sales and the costs for a certain product for this month are as shown in the table below. When the unit sales price is changed from 1,000 yen to 800 yen, in order to avoid making a loss, at least how many units need to be sold each month? Here, the fixed cost and the variable cost per unit of the product do not change.
Explanation
6,000 units — at the new price each unit contributes only 100 yen towards the fixed cost of 600,000 yen.
- •Contribution margin per unit at the new price: 800 − 700 = 100 yen
- •Break-even quantity: 600,000 ÷ 100 = 6,000 units
- •Check: sales 6,000 × 800 = 4,800,000 yen, costs 600,000 + 6,000 × 700 = 4,800,000 yen, profit 0
At the old price the product was already exactly at break-even: 2,000 units × 300 yen margin = 600,000 yen. Cutting the price by 20% cuts the margin by two thirds, so the volume must triple.
Answer (d)
Why not others:
- •(a) 2,400 — raises the volume by the same 20% as the price cut, 2,000 × 1.2; it covers only 2,400 × 100 = 240,000 yen of the fixed cost
- •(b) 2,500 — keeps sales at 2,000,000 yen, 2,000,000 ÷ 800, ignoring that each unit still costs 700 yen; the loss is 350,000 yen
- •(c) 4,800 — the break-even sales amount, 600,000 ÷ (1 − 700 ÷ 800) = 4,800,000 yen, divided by the old price of 1,000 yen instead of the new 800 yen
Key rule: Break-even quantity is fixed cost ÷ (unit price − unit variable cost); a small price cut shrinks the margin by far more in relative terms, so the required volume rises sharply.
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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.