A dishonest dealer defrauds his seller and buyer by using forged weights to the extent of 20%. His true gain per cent is

When a dealer cheats both the seller (while buying) and the buyer (while selling) by a percentage $x$, the overall gain percentage can be calculated using the successive percentage formula:
$$\text{Total Gain \%}=x+x+\frac{x\times x}{100}$$

Given $x=20\%$:

$$\text{Total Gain \%}=20+20+\frac{20\times 20}{100}$$

$$\text{Total Gain \%}=40+\frac{400}{100}=40+4=44\%$$

Thus, his true gain percent is $44\%$.