Question

A rich merchant had collected many gold coins. He did not want anybody to know about him. One day, his wife asked, "How many gold coins do we have?" After a brief pause, he replied, "Well! If I divide the coins into two unequal numbers, then 48 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 the merchant has?

• A. 96
• B. 53
• C. 43
• D. 45

Hint:

Factorizing expressions involving squares can simplify the solution process.

Answer 1

The Correct Option is C

Let the two unequal numbers be \( x \) and \( y \). From the given condition: \[ 48(x - y) = x^2 - y^2 \] Since \( x^2 - y^2 = (x - y)(x + y) \), we can simplify the equation to: \[ 48(x - y) = (x - y)(x + y) \] Canceling \( (x - y) \) from both sides (assuming \( x \neq y \)): \[ 48 = x + y \] Thus, the merchant has 43 coins.