This question's explanation and your answers so far.
ある商品の販売計画及び販売実績は表のとおりとなった。このとき，利益の計画に対する実績の比率は何％か。ここで，比率の小数点以下は切り捨てて求めるものとする。
| 販売計画 (X) | 販売実績 (Y) | 販売実績／販売計画 (Y／X) | |
|---|---|---|---|
| 仕入価格 (a) | 1,000 円 | 1,000 円 | 100% |
| 仕入数 (b) | 1,000 個 | 1,100 個 | 110% |
| 販売価格 (c) | 1,500 円 | 1,350 円 | 90% |
| 販売数 (d) | 1,000 個 | 1,100 個 | 110% |
| 利益 (e=c×d−a×b) | 50 万円 |
注記 網掛けの部分は，表示していない。
正解 Profit is found by 'selling price × sales quantity − purchase price × purchase quantity.' First, the planned profit is 1,500 yen × 1,000 units − 1,000 yen × 1,000 units = 500,000 yen, which matches the 500,000 yen in the table. Next, the actual profit, from a selling price of 1,350 yen, a sales quantity of 1,100 units, a purchase price of 1,000 yen, and a purchase quantity of 1,100 units, is 1,350 × 1,100 − 1,000 × 1,100 = 1,485,000 − 1,100,000 = 385,000 yen (= 385 thousand yen). Since the question asks for the ratio of actual to plan, actual ÷ plan ＝ 385,000 ÷ 500,000 ＝ 0.77. Expressed as a percentage this is 77%, and truncating the fractional part gives 77. Therefore the correct answer is ア.
99 is the ratio of 'sales revenue (selling price × sales quantity),' not of profit. Dividing the actual revenue 1,350 × 1,100 = 1,485,000 yen by the planned revenue 1,500 × 1,000 = 1,500,000 yen gives 99%, but the question asks for the ratio of profit after subtracting the purchase cost, so this is incorrect.
110 mistakenly takes the table's 'sales quantity (actual/plan = 110%)' value directly as the profit ratio. Even though the sales quantity is 1.1 times, because the selling price has dropped to 90%, profit does not increase at the same ratio; the profit ratio is 77%, so this is incorrect.
129 is the value obtained by swapping the denominator and numerator of the ratio. Calculating plan ÷ actual ＝ 500,000 ÷ 385,000 ≈ 1.298 by mistake yields about 129%. The question asks for 'actual relative to plan (actual ÷ plan),' so the direction is reversed; the correct value is 77%.