By selling articles at 7 for a rupee, a man loses 40%. To gain 40%, how many…

Concept: Profit or loss percentage is always calculated on the cost price (CP): Loss% = ((CP − SP) / CP) × 100, and Gain% = ((SP − CP) / CP) × 100. When articles are sold at a rate of n per rupee, the selling price per article is 1/n rupee (the unitary method).

1. Selling 7 articles for a rupee fixes the first selling price at SP1 = 1/7 rupee per article.

2. A loss of 40% means SP1 is 60% of the cost price: SP1 = 0.6 × CP, so CP = SP1 / 0.6 = (1/7) ÷ (3/5) = 5/21 rupee per article.

3. To gain 40%, the new selling price must be SP2 = 1.4 × CP = 1.4 × (5/21) = 7/21 = 1/3 rupee per article.

4. Since SP2 = 1/3 rupee per article, the number of articles that must be sold for one rupee is 1 ÷ SP2 = 3.

Cross-check: with CP = 5/21 rupee, selling 3 articles for a rupee gives SP = 1/3 rupee. Gain% = ((1/3 − 5/21) / (5/21)) × 100 = ((2/21) / (5/21)) × 100 = 40%, which matches the required gain — confirming the working.

So he must sell 3 articles for a rupee.