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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 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?
Let $$x$$ and $$y$$ be the 2 unequal number in which he divides the gold such that x>y.
Total coins with him = $$x+y$$
As per the merchant
$$48\left(x-y\right)\ =\ x^2-y^2$$
$$48\left(x-y\right)\ =\left(x-y\right)\left(x+y\right)$$
Either $$x+y = 48$$ or $$ x=y$$(rejected as it is given that they are unequal
hence merchant has 48 coins.
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