A vegetable vendor by means of his false balance defrauds to the extent of 10% in buying goods and also defrauds to 10% in selling, then the gain percent is

It is given that the vegetable vendor by means of his false balance defrauds to the extent of 10% in buying goods.

So, if the vegetable vendor is buying 100 gm goods then he is buying 10 gm (10% of 100 = 10) extra good.

So, multiplying factor for profit % in this case = $$\left(1+\dfrac{10}{100}\right)$$

Now while selling, he defrauds to 10% in selling

So, if the vegetable vendor is claiming to sell 100 gm goods then in reality he is selling 90 gm (since, he defrauds 10%)

So, the profit he made = (100-90) gm = 10 gm

So, multiplying factor for profit % in this case = $$\left(1+\dfrac{10}{90}\right)$$

So, overall gain % = $$\left(1+\dfrac{10}{100}\right)\left(1+\dfrac{10}{90}\right)-1=\dfrac{110}{100}\times\ \dfrac{100}{90}-1=\dfrac{11}{9}-1=\dfrac{2}{9}$$

So, gain% = $$\dfrac{2}{9}\times\ 100\%=22\dfrac{2}{9}\%$$