This question's explanation and your answers so far.
計画時の予算が2,000万円で，40日間で100本のプログラムを作成するプロジェクトがある。プロジェクトが20日経過した時点で全体の40%である40本のプログラムが完成し，1,000万円のコストが掛かった。プロジェクトの指標を次の評価式で算出する場合，プロジェクトの指標として適切な組合せはどれか。ここで，各プログラムの作成に必要な日数及びコストは全て同一で，プロジェクト期間中は常に同じ量の作業が実施されるものとする。 〔評価式〕 スケジュール（％）： （完成したプログラム本数÷評価時点での完成見込みプログラム本数）×100 コスト（％）： （完成したプログラムに掛かったコスト÷完成したプログラム分として計画したコスト）×100
正解 Calculate the schedule (%) and cost (%) exactly as the evaluation formulas specify. [Schedule] The plan is 100 programs in 40 days with a constant workload, so the number expected to be completed at day 20 (half of the period) is half of 100 = 50. The actual number completed is 40, so 40÷50×100 = 80%, indicating progress is behind the plan. [Cost] The planned cost per program is 20 million yen ÷ 100 = 0.2 million yen. The planned cost for the 40 completed programs is 0.2 million × 40 = 8 million yen. The actual cost incurred was 10 million yen, so 10÷8×100 = 125%. In other words, the same output (40 programs) was produced at a higher cost than planned, indicating a budget overrun. Therefore the combination of schedule 80% and cost 125%, choice 'ア', is correct.
Schedule 80% is correct, but cost 100% is wrong. The planned cost for the 40 completed programs is 8 million yen, while the actual cost is 10 million yen, so it is not 100% (on plan) but 125% (over budget). Mistaking the actual cost for the planned cost leads to the erroneous figure of 100%.
Cost 125% is correct, but schedule 90% is wrong. The number expected to be completed is 'the number that should have been completed at the time of evaluation (day 20 = half of the period) = 50,' so 40÷50×100 = 80%. Dividing by some other value instead of 50 (for example, relating the 40 completed programs to the total) produces the incorrect figure of 90%.
Both schedule 90% and cost 100% are wrong. The schedule should be 40÷50×100 = 80% (50 expected), and the cost should be 10÷8×100 = 125% (planned cost 8 million yen); both figures have the wrong calculation basis.