A fruitseller by means of a false balance cheats A fruitseller by means of a false balance cheats $20$% in buying fruits and also cheatz buyer to the same extent in selling. Find the gain percent on his outlay. My attempt: While buying $1$ kg, $$=1+\frac{20}{100} \times 1$$ $$=\frac{6}{5}$$ While selling $1$ kg, $$1-\frac{20}{100} \times 1$$ $$=\frac{4}{5}$$. Now, what should I do next?

Lets assume the original price to be $x$.

If the fruit seller was honest $$ 1 kg \rightarrow x $$ Since he cheats 20% while buying $$ 1 kg \rightarrow 4x/5 $$ Also he cheats 20% while selling
$$ 1 kg \rightarrow 6x/5 $$ His net profit is $$ 6x/5 - 4x/5 = 2x/5 $$ Gain percent is (Profit/Cost Price)*100 $$ \frac{2x/5}{4x/5}*100 = 50\% $$ His gain percent is 50%