This question's explanation and your answers so far.
A作業, B作業, C作業からなる図のような業務プロセスがある。情報システムを導入することで改善が実現できるとき, 製品を1個製造するために必要な作業工数は改善前に比べて何%削減されるか。ここで, 図の矢印は作業順序を表し, 作業工数は要員数×作業時間で計算する。 図(業務プロセス): A作業 → C作業, B作業 → C作業（A作業とB作業がいずれもC作業に先行する） 〔改善前〕 ・各作業の要員数は10名 ・製品1個当たりの所要作業時間は, A作業は3時間, B作業は3時間, C作業は4時間である。 〔改善後〕 ・A作業に必要な要員数が半分になる。 ・C作業の製品1個当たりの所要作業時間が半分になる。
15 counts only the reduction in operation A. Operation A goes from 30 person-hours to 15 person-hours, a reduction of 15 person-hours, but this misses the 20 person-hour reduction in operation C, which goes from 40 person-hours to 20 person-hours. Two improvement conditions are given, so both must be reflected in the effort.
20 counts only the reduction in operation C. The time required for operation C goes from 4 hours to 2 hours, so its effort goes from 40 person-hours to 20 person-hours, a reduction of 20 person-hours, but this misses the 15 person-hour reduction produced by halving the personnel of operation A. This is the opposite oversight from ア, and it too looks at only one of the improvements.
In this question the total effort before the improvement is exactly 100 person-hours, so the number of person-hours reduced is directly the reduction rate in percent. 30 is what you get if you mistake the reduced effort for 30 person-hours: for example, if you over-read “the number of personnel required for operation A is halved” as “operation A (30 person-hours) becomes unnecessary altogether” and at the same time miss the 20 person-hour reduction in operation C. What is actually reduced is 15 person-hours for operation A plus 20 person-hours for operation C, 35 person-hours in total; and even when the personnel of operation A goes from 10 to 5, the 3 hours of work itself remains, so its 30 person-hours do not disappear entirely.
正解 Work effort is found as number of personnel x operation time, and the effort of the three operations A, B, and C is added up. Before the improvement: operation A is 10 people x 3 hours = 30 person-hours, operation B is 10 people x 3 hours = 30 person-hours, and operation C is 10 people x 4 hours = 40 person-hours, for a total of 100 person-hours. After the improvement: the number of personnel for operation A is halved, so 5 people x 3 hours = 15 person-hours; operation B is unchanged, so it stays at 30 person-hours; and the operation time for operation C is halved, so 10 people x 2 hours = 20 person-hours, for a total of 65 person-hours. The effort reduced is therefore 100 - 65 = 35 person-hours, and the reduction rate is 35 / 100 x 100 = 35%. So エ (35) is correct. Note that the arrows in the figure only show the order of operations, namely that operation A and operation B precede operation C; they do not affect the total effort itself (even for operations carried out in parallel, the person-hours put into both are added together).