ITPEC IP April 2025 Question 67

Topic: Corporate ActivitiesAlso asked in October 2019, Spring 2021 and April 2023

A certain product’s sales plan and sales result are shown in the table below. What is the ratio in percentage of the profit result to the profit plan? Here, the decimal fractions of the ratio are truncated.

Sales plan(X)Salesresult(Y)Salesresult /salesplan(Y/X)Purchase price(p)1,000 yen1,000 yen100%Number ofpurchases (q)1,000pieces1,100pieces110%Sale price (r)1,500 yen1,350 yen90%Number of sales(s)1,000pieces1,100pieces110%Profit(t = r × s - p × q)500,000yen

Note: The shaded section is not shown.

Explanation

77% — compute the actual profit with the formula in the table, then divide it by the planned 500,000 yen.

  • •Actual sales: 1,350 × 1,100 = 1,485,000 yen
  • •Actual purchase cost: 1,000 × 1,100 = 1,100,000 yen
  • •Actual profit: 1,485,000 − 1,100,000 = 385,000 yen
  • •Ratio: 385,000 ÷ 500,000 = 0.77, that is 77%

The 10% rise in volume cannot make up for the 10% cut in price, because the cut comes entirely out of the 500-yen margin: each piece now earns only 350 yen.

Answer (a)

Why not others:

  • •(b) 99 — the ratio of sales revenue, 90% × 110%, or 1,485,000 ÷ 1,500,000; it ignores the purchase cost
  • •(c) 110 — the ratio of the number of sales alone
  • •(d) 129 — the ratio inverted, plan over result: 500,000 ÷ 385,000, truncated

Key rule: Profit is a small difference between two large numbers, so a small change in price moves it by far more in percentage terms than it moves sales.

Corporate Activities · AI-written, may contain errors

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