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First let the fraction be a/b, where b not = 0.
We start with the first bit of information:
If the numerator is multiplied by three and the denominator reduced by three we get 18/11 translates to
if the numerator is increased by eight and denominator is doubled we get 2/5 translates to
cross multiply in both (i) and (ii) to get
pull the a and b parts to one side as
multiply (v) by 2 and (vi) by -9 to get
add down to get
So, a = 12
Sub this into (iv) we get
solving for b, we get
b = 25.
So our original fraction is