An article is sold at a profit of 49%. If the cost price is increased by ₹40…

Concept: When an article is sold at a profit of p%, the selling price (SP) relates to the cost price (CP) as SP = CP × (1 + p/100). If both the cost price and selling price are changed by fixed amounts, the new profit percentage is obtained by applying the same relation to the new CP and new SP.

1. Let the original cost price be ₹CP. Since the article is sold at a profit of 49%, the selling price is SP = 1.49 × CP.

2. The new cost price becomes CP + 40, and the new selling price becomes SP − 55.

3. At the new prices, the profit is 47.5%, so SP − 55 = 1.475 × (CP + 40).

4. Substituting SP = 1.49 × CP: 1.49CP − 55 = 1.475CP + 1.475 × 40 = 1.475CP + 59.

5. Collecting CP terms: 1.49CP − 1.475CP = 59 + 55, which gives 0.015 × CP = 114.

6. Solving for CP: CP = 114 ÷ 0.015 = ₹7,600.

Cross-check: With CP = ₹7,600, SP = 1.49 × 7,600 = ₹11,324. The new cost price is ₹7,640 and the new selling price is ₹11,324 − 55 = ₹11,269. The new profit = (11,269 − 7,640) ÷ 7,640 × 100 = 47.5%, matching the condition given in the question.

So, the original cost price of the article is ₹7,600.