平成24年度 秋期 ITパスポート試験 問87

※ Our check while writing this explanation could not fully confirm the published answer; scoring follows IPA's official key.

• ×Incorrectア

  770 is the increase obtained when the same calculation is done for the oyakodon (chicken and egg bowl), not the beef bowl. The oyakodon has a unit price of 450 yen, a cost of 250 yen, a sales volume of 2,310 servings, and a gross profit of 462,000 yen, so after the 50 yen discount its gross profit per serving is 450 − 50 − 250 = 150 yen, the required volume is 462,000 ÷ 150 = 3,080 servings, and the increase is 3,080 − 2,310 = 770 servings. This is the value you would pick if you read the wrong row of Figure 1, and it does not satisfy the condition for the beef bowl. If only 4,800 + 770 = 5,570 beef bowls were sold, the gross profit would be just 150 × 5,570 = 835,500 yen, short of this month's 960,000 yen.

• ×Incorrectイ

  880 is the increase obtained when the same calculation is done for the curry, not the beef bowl. The curry has a unit price of 400 yen, a cost of 150 yen, a sales volume of 3,520 servings, and a gross profit of 880,000 yen, so after the 50 yen discount its gross profit per serving is 400 − 50 − 150 = 200 yen, the required volume is 880,000 ÷ 200 = 4,400 servings, and the increase is 4,400 − 3,520 = 880 servings. Because it is a row with the same 400 yen unit price as the beef bowl it is easy to confuse the two, but its cost of 150 yen is different, so the value is different as well. If 4,800 + 880 = 5,680 beef bowls were sold, the gross profit would be 150 × 5,680 = 852,000 yen, below this month's 960,000 yen, so the condition would not be met.

• ○ウ

  正解 The correct answer is ウ “1,600”. According to the worksheet in Figure 1 of question group A, the beef bowl has a unit price of 400 yen, a cost of 200 yen, and a sales volume of 4,800 servings this month. Gross profit is found by “(unit price − cost) × sales volume”, so this month's gross profit per beef bowl is 400 − 200 = 200 yen, and this month's gross profit is 200 × 4,800 = 960,000 yen (which matches the 960,000 in the gross profit column of Figure 1). The key point here is that only the unit price is discounted; the cost, such as the cost of ingredients, stays at 200 yen. Next month's unit price becomes 400 − 50 = 350 yen, so the gross profit per serving drops to 350 − 200 = 150 yen. In other words, the 50 yen discount becomes exactly the decrease in gross profit per serving. Letting x be the sales volume needed next month to earn 960,000 yen of gross profit or more, we have 150 × x ≧ 960,000, so x ≧ 6,400 servings. What the question asks is not the required volume itself but the increase — “by at least how much it must go up compared with this month” — so the answer is 6,400 − 4,800 = 1,600 servings. In fact, if 6,400 servings are sold, the gross profit is 150 × 6,400 = 960,000 yen, exactly the same as this month, confirming that this is the smallest value satisfying the condition.

• ×Incorrectエ

  3,450 is an excessive value. In this case next month's sales volume would be 4,800 + 3,450 = 8,250 servings and the gross profit would be 150 × 8,250 = 1,237,500 yen, far above this month's 960,000 yen. The gross profit condition itself would be satisfied, but the question asks “by at least how much it must increase”, that is, the smallest increase, and the smallest value satisfying the condition is 1,600 servings, so this choice is wrong. Dividing 960,000 yen by the post-discount gross profit of 150 yen per serving determines the required volume uniquely as 6,400 servings; 8,250 servings cannot be derived from any correct calculation.