At 82 bowls, the after-reduction gross profit is only 320 × 82 = 26,240 yen, which falls short of the pre-reduction 27,750 yen and cannot exceed it, so it is wrong.
×Incorrectイ
Even at 84 bowls, it is 320 × 84 = 26,880 yen, still below the pre-reduction 27,750 yen and unable to exceed it, so it is wrong.
○ウ
正解Gross profit is found by “(unit price − cost) × sales volume.” From the shared table, char siu ramen has a unit price of 800 yen, a cost of 430 yen, and a sales volume of 75 bowls, so the per-bowl gross profit before the price reduction is 800 − 430 = 370 yen, and the gross profit is 370 × 75 = 27,750 yen. Reducing the unit price by 50 yen makes the unit price 750 yen, and since the cost of 430 yen stays the same, the per-bowl gross profit after the reduction falls to 750 − 430 = 320 yen. The smallest sales volume N that exceeds the pre-reduction gross profit of 27,750 yen satisfies 320 × N > 27,750, giving N > 86.7…, so the smallest integer is 87 bowls (320 × 86 = 27,520 yen falls short, while 320 × 87 = 27,840 yen is the first to exceed 27,750 yen). Therefore the correct answer is choice ウ, 87.
×Incorrectエ
At 90 bowls it is 320 × 90 = 28,800 yen, which does exceed 27,750 yen, but 87 bowls also exceeds it, so 90 is not the “smallest sales volume” and is wrong (it satisfies the condition but is larger than necessary).
ここがポイント
Gross profit = (unit price − cost) × sales volume. A price reduction lowers only the unit price while the cost stays the same, so the per-bowl gross profit drops; you make up for that drop by increasing sales volume and find the smallest quantity that exceeds the original gross profit.
Since the condition is “exceed (>),” round 27,750 ÷ 320 = 86.7… up to the smallest integer 87 (not equality, but the smallest integer strictly greater).