An article sells for Rs.65 the price gives the retailer a profit of 30% on his cost. What will be the new retail price if he cuts his profit to 10% of the cost

Start with the cost price. A profit of 30% on cost means the selling price is 130% of cost, so 1.3 × C = 65, which gives C = Rs. 50.

At a 10% profit on cost, the new selling price is 1.1 × 50 = Rs. 55, so D is correct.

• A) Rs. 42 is below cost. It would mean a loss of 16%, not a profit.
• B) Rs. 45.5 comes from taking 30% off the Rs. 65 selling price (65 × 0.7). The percentage is applied to the wrong base. Profit is always calculated on cost here.
• C) Rs. 50 is the cost price itself. Selling at this price gives zero profit.

The core concept is the difference between markup on cost and margin on selling price. Under the Prelims-level formula, profit % = (SP − CP)/CP × 100. The same idea appears in Mains-oriented commercial and economic reasoning, such as tracing how cost-based pricing affects consumer prices.

Trap: candidates subtract 30% from the given selling price instead of first recovering the cost price, and so pick B.