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From Mahavira (Posted on 2017-07-18) Difficulty: 2 of 5
From the year c. 850 the book Ganita-Sara-Sangraha contains the following:

Three merchants saw in the road a purse. One said, "If I secure this purse, I shall become twice as rich as both of you together."
Then the second said, "I shall become three times as rich."
Then the third said, "I shall become five times as rich."
What is the value of the money in the purse, as also the money on hand?

There are an infinite number of solutions. Find the smallest whole number amounts the merchants could have.

No Solution Yet Submitted by Jer    
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Hints/Tips re(2): Simple Solution, simple-yes ... correct-Yes | Comment 6 of 11 |
(In reply to re: Simple Solution, simple-yes ... correct-no by Ady TZIDON)

There is no issue.  Bert says "I shall become three times as rich"  That implies his total wealth, let that amount be x.  After acquiring the purse would be three times his wealth, which is 3x.  This implies the purse contained twice Bert's wealth, which makes the purse 2x.

I say your interpretation is wrong.  Your position is saying the purse contains 3x.  But if that were the case Bert would need to say acquiring the purse would increase his wealth by three times his original amount, but his statement implies his wealth after acquiring the purse would triple which includes his original wealth of x.

  Posted by Brian Smith on 2017-07-19 08:45:40
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