whodunnit puzzle


494 / 858 = ·575757575757...

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Note: It is the only possible correct answer from a vast choice of fractions.
Algebra rather than a brute force approach solves it.

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Replace the alphabets in the fraction EVE/DID = .IT
Let .ITITIT be X....(1)
Multiplying by 100, we get 100X = IT.ITIT ....(2)
(2) - (1) gives 99X = IT
So, EVE / DID = IT/99
99 * EVE = IT * DID
Either IT or DID should be a multiple of 11
IT cannot be , so DID is, which implies 2D = I or 2D - I = 11
but IT * DID is divisble by 99
so if IT is divisble by 9

DID may be(121,242,363,484,616,737,858, 979)
IT may be ( 18,27,36,45,54,63,72,81)

But DID*IT /99 should result in EVE
but 121*27,242*45,363*63,484*81,616*18,737*36,858*54,979*72
dont result in the pattern EVE when divided by 99

or IT and DID are both divisible by 3
Giving DID ={363} and IT={60,63,69} or
Giving DID ={858} and IT={51,54,57}

and of the above only 858*57/99 gives 494(EVE)
Finally we have 494/858 = 0.5757575757


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