A dishonest dealer professes to sell his goods at cost price. But he uses a false weight and thus gains $$6\frac{18}{47}\%$$ . For a kg, he uses a weight of

Let the amount of grams shopkeeper cheats for 1000 gm be X gm .

So, he sells only (1000-X) gms  to customer at a selling price given to be equal to CP.
The original Cost Price which would have costed shopkeeper =$$\dfrac{\ CP}{1000}\left(1000-X\right)$$

Therefore , Profit % =$$\ \dfrac{CP-\frac{\ CP}{1000}\left(1000-X\right)\ }{\dfrac{\ CP}{1000}\left(1000-X\right)\ }$$ x 100%

                              = $$\dfrac{\ X}{1000-X}\times100$$

        $$\dfrac{\ X}{1000-X}\times100\%$$ = $$6\dfrac{18}{47}\%$$
             
         $$\dfrac{\ X}{1000-X}=\dfrac{\ 3}{47}$$

X = 60 gms .

Therefore (1000-60) = 940 gm