Profit Calculation During Festive Sale

This problem calculates the final profit percentage after a dining table's price is adjusted during a festive sale. Key steps involve understanding initial profit, price elevation, and discount application.

Pricing Stages Explained

Initial Sale: The dining table was sold at price $₹X$, achieving a $25%$ profit over its Cost Price ($CP$). This means $X = CP \times (1 + 0.25)$ or $X = 1.25 \times CP$.

Festive Sale: The marked price was elevated to $₹Y$. A promotional $20%$ discount was then applied to this marked price $Y$. The final Selling Price ($SP_final$) is calculated as $SP_final = Y \times (1 - 0.20)$, which simplifies to $SP_{final} = 0.80Y$.}

The objective is to determine the percentage profit achieved relative to the original CP during this festive sale period.

Step-by-Step Calculation

To simplify calculations, let's assume the Cost Price (CP) of the dining table is $₹100$.

1. Calculate the Initial Selling Price ($X$): Given a $25%$ profit margin: $X = 100 \times (1 + 0.25) = ₹125$.
2. Define the Festive Sale Final Selling Price ($SP_final$): The price after a $20%$ discount on the marked price $Y$ is: $SP_{final} = Y \times (1 - 0.20) = 0.80Y$.
3. Determine the required $SP_final$ for a $60%$ Profit: For the festive sale, if the profit is $60%$, the final selling price must be: $SP_{final} = CP \times (1 + \text{Target Profit Rate}) = 100 \times (1 + 0.60) = ₹160$.
4. Calculate the Marked Price ($Y$): By equating the expressions for $SP_final$ from steps 2 and 3: $0.80Y = 160$ Solving for $Y$: $Y = \frac{160}{0.80} = ₹200$. This confirms the marked price was elevated ($₹200$ is greater than the initial sale price $₹125$).
5. Calculate the Final Percentage Profit: The final selling price is $₹160$ and the cost price is $₹100$. $\text{Profit} = SP_{final} - CP = 160 - 100 = ₹60$. The percentage profit is calculated as: $\text{Percentage Profit} = \frac{\text{Profit}}{CP} \times 100\% = \frac{60}{100} \times 100\% = 60\%$.