Let the original price of the sugar be 100x, ⇒ After 20% decrease, price would be 80x ⇒ Ratio = 100x ∶ 80x = 5x ∶ 4x Due to this a family purchases 20 kg more sugar for Rs. 400, ⇒ x = 20 ⇒ original consumption of sugar = 20 × 4 = 80 kg ∴ original price of sugar = 400/80 = Rs. 5/kg Alternative solution: Let the original price of 1 kg sugar be x and quantity purchased for Rs. 400 be y kg So, xy = 400 When price is reduced by 20%, price of 1 kg sugar = 0.8x and the quantity of sugar purchased for Rs. 400 will be y + 20 kg So, (0.8x) × (y + 20) = 400 0.8xy + 16x = 400 320 + 16x = 400 16x = 80 ∴ x = Rs. 5/Kg