Multiple choice general knowledge math & puzzles

A rich merchant had collected many gold coins. He did not want anybody to know about them. One day, his wife asked, "How many gold coins do we have?" After pausing a moment, he replied, "Well! If I divide the coins into two unequal numbers, then 32 times the difference between the two numbers equals the difference between the squares of the two numbers." The wife looked puzzled. Can you help the merchant's wife by finding out how many gold coins they have?

  1. 22

  2. 25

  3. 32

  4. 35

  5. 42
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the two unequal numbers be x and y (x ≠ y). Condition: 32(x-y) = x² - y². Using difference of squares: x² - y² = (x+y)(x-y). So 32(x-y) = (x+y)(x-y). Since x ≠ y, we can divide by (x-y): x+y = 32. For positive integers dividing into two unequal numbers, x+y=32 means the total is 32 coins. Option C is correct.

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