An article is sold at 20% profit. If its cost price is increased by ₹50 and at…

Profit percentage is defined relative to cost price: Profit % = ((SP − CP) / CP) × 100. When both the cost price and selling price change, the new profit percentage must be recalculated from the new cost price and new selling price — it does not simply shift by adding or subtracting the stated change from the old percentage without re-deriving the ratio.

Let the original cost price be ₹x.

1. Since the original profit is 20%, the original selling price is SP = 1.2x.

2. The new cost price is CP' = x + 50, and the new selling price is SP' = 1.2x + 30.

3. The new profit percentage is 20% − 3(1/3)% = 50/3% (here, the drop of 3(1/3)% is read as 3(1/3) percentage points, the standard interpretation for this classic problem type).

4. Apply the profit formula to the new values: ((SP' − CP') / CP') × 100 = 50/3.

5. Substitute the expressions: ((1.2x + 30 − (x + 50)) / (x + 50)) × 100 = 50/3, which simplifies to (0.2x − 20)/(x + 50) = 1/6.

6. Cross-multiply: 6(0.2x − 20) = x + 50, giving 1.2x − 120 = x + 50.

7. Solve: 0.2x = 170, so x = 850.

Verify: with CP = ₹850, SP = 1.2 × 850 = ₹1,020, giving a profit of exactly 20%. After the increases, the new CP = ₹900 and new SP = ₹1,050, giving a profit of (1,050 − 900)/900 × 100 = 50/3% ≈ 16.67%, exactly 3(1/3)% less than the original 20%. This confirms the cost price is ₹850.