DRDO Multi tasking staff Model paper 10

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