A merchant has 5000 kg of Basmati rice.

Let the quantity sold at 20% profit be $ x $ kg, and at 35% profit be 5000 - $ x $ kg

Using allegation: $\frac{35 - 29}{29 - 20} = \frac{6}{9} = \frac{2}{3} $

Ratio of quantities sold at 20% and 35% profit = 2 : 3

$ x : (5000 - x) = 2 : 3 $

$ \frac{x}{5000 - x} = \frac{2}{3} $

$ 3x = 2(5000 - x) $

$ 3x = 10000 - 2x $

$ 5x = 10000 $

$ x = 2000 $ kg

$ 5000 - x = 3000 $ kg

Quantity at 20% profit = 2000 kg, at 35% profit = 3000 kg