A shopkeeper sells rice at the cost price, but uses false weight. He gains 20% in this process. What weight does he uses for one kilogram?

Let say cost price(C.P) of 1 kg(1000 g) of rice be Rs. 100

Given Shopkeeper is selling rice  at cost price,

$$\Rightarrow$$ Selling price(S.P) = C.P = Rs. 100

If he had used correct weight of 1000 g then C.P would have also been Rs. 100.

But given that he uses false weight. Let the weight he had used be  'x' g.

For 1000 g of rice  the C.P = Rs. 100

$$\Rightarrow$$ For '1' g of rice the C.P will be Rs. $$\frac{1}{10}$$

$$\Rightarrow$$ For 'x' g of rice the C.P will be Rs. $$\frac{x}{10}$$

Given that, by using this false weight the shop keeper gains 20%.

Gain percentage = $$\frac{S.P - C.P}{C.P}\times 100$$

$$\Rightarrow \frac{20}{100} = \frac{S.P - C.P}{C.P}$$

$$\Rightarrow S.P = 1.2\times C.P$$

$$\Rightarrow 100 = 1.2\times \frac{x}{10}$$

$$\Rightarrow x = 833.33$$ 

Hence the false weight used is 833.33 g