A shopkeeper sold sarees at ₹ 266 each after giving 5% discount on labelled price. Had he not given the discount, he would have earned a profit of 12% on the cost price. What was the cost price of each saree?

### Concept & Marked Price Determination We first determine the Marked Price (labelled price) from the discounted Selling Price, then use the "no discount" scenario to find the Cost Price. $$ \text{MP} = \frac{\text{SP}}{1 - D\%} $$ ### Step-by-Step Solution * The Selling Price (SP) of each saree after a 5% discount is ₹ 266. * Marked Price (MP) = $\frac{266}{1 - 0.05} = \frac{266}{0.95} = 280$. * Had he not given the discount, he would sell the saree at the MP, meaning the new SP = ₹ 280. * At this new SP, the profit would be 12% on the Cost Price (CP). * Cost Price (CP) = $\frac{\text{New SP}}{1 + P\%} = \frac{280}{1.12}$. * Solving for CP: $\frac{280}{1.12} = \frac{28000}{112} = 250$. * The cost price is ₹ 250, which does not match options (a), (b), or (c). ### Exam Strategy & Shortcut Calculate $\text{MP} = \frac{266}{0.95}$. Notice that $266 = 133 \times 2 = 19 \times 7 \times 2$. Since $95 = 19 \times 5$, $\frac{266}{95}$ simplifies cleanly to $\frac{14}{5} = 2.8$, making MP = 280. Then $\text{CP} = \frac{280}{1.12} = 250$. Fast mental calculation of these ratios saves time. ### Common Pitfall Selecting "Data inadequate" when the calculated answer doesn't appear in the numeric choices, rather than correctly choosing "None of these". ### Final Answer Therefore, the correct answer is **None of these**.