How Many Gold Coins? - Answer

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HOW MANY 

GOLD COINS? 

- ANSWER

Age group: All

The question was:

"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 67 times the difference between the two numbers equals the difference between the squares of the two numbers.'

His wife looked puzzled. Can you help the merchant's wife by finding out how many gold coins they have?"


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Now coming to the Answer!

Let the two unequal parts be x and y.
We have to find the total number of coins i.e. (x+y).

From the given statement:
67 times the difference (x-y) = difference between squares of two numbers (x^2 - y^2)

i.e. 67(x-y) = x^2 - y^2

The only property you need to use is a^2 - b^2 =  (a+b)(a-b), which gives us:

67*(x-y) = (x+y)*(x-y)

Dividing by (x-y) on both sides,
67 = x+y

Therefore, the total number of coins is 67.

Wasn't that easy?

If you have got the same answer in any other way, then do let me know in the comments section!

If you have interpreted this question in another suitable way, then do let me know in the comments section again!

If I have made any significant errors, do let me know about that too, and I will be sure to make the necessary changes!
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I hope you enjoyed this :)


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With Warm Wishes,
Lavanya


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