Study the table and find the ratio P : R .

Profit percentage is defined as Profit% = ((Selling Price − Cost Price) / Cost Price) × 100. When a cost price is marked up by x% to form the marked price and then a discount of y% is applied to that marked price, the selling price becomes CP × (1 + x/100) × (1 − y/100) — the two percentage changes combine multiplicatively, not by simple addition or subtraction.

1. Article 1's marked price = 12000 × (1 + 20/100) = 12000 × 1.20 = 14400.

2. Apply the 10% discount on the marked price: Selling Price M = 14400 × (1 − 10/100) = 14400 × 0.90 = 12960.

3. Profit percentage P = ((12960 − 12000) / 12000) × 100 = (960 / 12000) × 100 = 8%.

4. Article 3's marked price = 13000 × (1 + 30/100) = 13000 × 1.30 = 16900.

5. Apply the 20% discount on the marked price: Selling Price O = 16900 × (1 − 20/100) = 16900 × 0.80 = 13520.

6. Profit percentage R = ((13520 − 13000) / 13000) × 100 = (520 / 13000) × 100 = 4%.

7. Ratio P : R = 8 : 4 = 2 : 1.

As an independent check, a mark-up of x% followed by a discount of y% on the marked price is equivalent to one net percentage change of (x − y − xy/100)%. For Article 1: 20 − 10 − (20 × 10)/100 = 8%, which matches P. For Article 3: 30 − 20 − (30 × 20)/100 = 4%, which matches R. So P : R = 8 : 4, which simplifies to 2 : 1.