The double displacement reaction produces barium sulphate (BaSO$_4$) as a solid precipitate, not sodium chloride. Sodium chloride stays dissolved in water. The Assertion is accurate regarding the reaction but misidentifies the precipitate. The Reason correctly defines a precipitate as an insoluble product in an aqueous reaction, but it doesn't accurately explain the incorrect Assertion. Consequently, the Assertion is correct, while the Reason is incorrect.