A rich merchant had collected many gold coins. He did not want anybodyto know about them. One day, his wife asked, "How many gold coins do wehave?"After pausing a moment, he replied, "Well! If I divide the coins intotwo unequal numbers, then 37 times the difference between the twonumbers equals the difference between the squares of the two numbers."The wife looked puzzled. Can you help the merchant's wife by findingout how many gold coins?

37(x-y) =x^2-y^2.
You no that x^2-y^2=(x-y)(x+y).
So (x-y) cancels on both sides to give
x+y=37.
so sum of unequal halves=37 which is the req answer.

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vivekbhc

  • Jul 21st, 2008
 

the merchant is having n gold coins
 he divides it into x and y
37times the difference is 37(x-y)
the squares of the two numbers is x^2 and y^2
   so 37(x-y)=X^2-Y^2   (X^2-Y^2 = x+y*x-y)
 solving we get x+y=37 ie the sum of the gold coins are 37
   the solution is 37

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