By selling a bicycle for ₹ 2850, a shopkeeper gains 14%. If the profit is reduced to 8% then the selling price will be (S.S.C., 2010)

### Concept & Proportionality in Selling Price The Selling Price (SP) is directly proportional to the percentage multiplier of the Cost Price (CP). Thus, we can avoid calculating the absolute CP by setting up a direct ratio between the two selling conditions. $$ \frac{SP_1}{100 + P_1} = \frac{SP_2}{100 + P_2} $$ ### Step-by-Step Solution * **Method 1: Direct Ratio** * Given $SP_1 = 2850$ corresponds to a profit of $14\%$. This means $2850 = 114\%$ of CP. * We need $SP_2$, which corresponds to a profit of $8\%$, meaning $SP_2 = 108\%$ of CP. * $\frac{SP_1}{114} = \frac{SP_2}{108}$ * $SP_2 = \left(\frac{2850}{114}\right) \times 108$ * $SP_2 = 25 \times 108 = 2700$ rupees. * **Method 2: Finding Cost Price First** * $CP = \frac{2850}{1.14} = 2500$ rupees. * New $SP = 2500 \times 1.08 = 2700$ rupees. ### Exam Strategy & Shortcut The unitary method is extremely fast here. If $114 \text{ units} = 2850$, then $1 \text{ unit} = \frac{2850}{114} = 25$. We need the value of $108 \text{ units}$. So, $108 \times 25$. To multiply by 25 quickly, multiply by 100 and divide by 4: $10800 / 4 = 2700$. ### Common Pitfall A common mistake is incorrectly calculating the base CP by taking $14\%$ off the selling price directly ($2850 \times 0.86$), which mathematically alters the base of the percentage. Always remember: $\text{SP} = \text{CP} \times (1 + \text{Profit \%})$. ### Final Answer Therefore, the correct answer is **₹ 2700**.