This question's explanation and your answers so far.
10か月で完成予定のソフトウェア開発プロジェクトにおいて，投入人数及び月末時点での進捗は表のとおりである。プロジェクトの立ち上がりで効率が悪かったことから，5月末時点の進捗が計画の50%に対して40%であった。4月以降の生産性が維持できるとすると，開発期限厳守のためには6月以降に必要な追加人員は最低何人か。ここで，追加人員の生産性は，既に投入済みの人員の4月以降の生産性と同じとする。 進捗（月末時点）
| 項目 | 投入人数 | 1月 | 2月 | 3月 | 4月 | 5月 | 6月 | 7月 | 8月 | 9月 | 10月 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 計画 | 10名 | 10% | 20% | 30% | 40% | 50% | 60% | 70% | 80% | 90% | 100% |
| 実績 | 10名 | 5% | 12% | 20% | 30% | 40% |
With only 1 additional person, the total becomes 11 people advancing 11% per month, which is only 55% over 5 months. 40+55=95%, which does not reach 100% and misses the deadline, so it is insufficient.
正解 First, find the “productivity from April onward” from the actual results. The actuals are 20% at end of March → 30% at end of April → 40% at end of May, meaning 10 people advance 10% each month. So productivity is 1% per person per month. Next, look at the remaining work: 40% is done at end of May, so 100−40=60% remains. The deadline is end of October, leaving 5 months: June, July, August, September, and October. To strictly meet the deadline, progress must be 60÷5=12% each month. With only the existing 10 people, only 10% is made each month, which is 2% short. Additional people also contribute 1% per person per month, so covering the 2% gap requires at least 2 additional people. Therefore the correct answer is イ (2 people).
5 is the number of months in the remaining period (5 months from June to October), not the number of additional people needed. Adding 5 people would advance 15% per month and 75% over 5 months, which is greatly excessive and does not satisfy the condition of the minimum number of people.
12 is the total number of people needed to advance 12% per month (12%÷1%＝12 people), not the additional people the question asks about. After subtracting the existing 10 people, 12−10＝2 people is the additional amount. This is a wrong answer that confuses the total number with the additional number.