A shopkeeper offered a discount of 15% on the labelled price. By selling an article for ₹ 340 after giving discount he earned a profit of $13 \frac{1}{3}\%$. What would have been the percent profit earned if no discount was offered?

### Concept & Profit Calculation When no discount is offered, the item is sold at its Marked Price (MP). $$ \text{Profit \%} = \frac{\text{MP} - \text{CP}}{\text{CP}} \times 100 $$ ### Step-by-Step Solution * The Selling Price (SP) is ₹ 340 after a 15% discount. * Marked Price (MP) = $\frac{\text{SP}}{0.85} = \frac{340}{0.85} = 400$. * The profit earned is $13 \frac{1}{3}\% = \frac{40}{3}\%$. * Cost Price (CP) = $\frac{\text{SP}}{1 + \text{Profit \%}} = \frac{340}{1 + \frac{40}{300}} = \frac{340 \times 300}{340} = 300$. * If no discount is offered, the new SP is the MP, which is ₹ 400. * Profit = $400 - 300 = 100$. * Profit % = $\frac{100}{300} \times 100 = 33 \frac{1}{3}\%$. ### Exam Strategy & Shortcut The ratio formula: $$ \frac{\text{MP}}{\text{CP}} = \frac{100 + \text{Profit \%}}{100 - \text{Discount \%}} $$ $$ \frac{\text{MP}}{\text{CP}} = \frac{100 + \frac{40}{3}}{85} = \frac{340}{3 \times 85} = \frac{340}{255} = \frac{4}{3} $$ If no discount is given, SP = MP. The profit is $\frac{4-3}{3} = \frac{1}{3} = 33 \frac{1}{3}\%$. Notice how we never needed to use the actual SP (₹ 340)! ### Common Pitfall Wasting time calculating the actual Marked Price and Cost Price when working purely with ratios avoids the tedious ₹ 340 calculation entirely. ### Final Answer Therefore, the correct answer is **$33 \frac{1}{3}$**.