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 ($SPfinal$) is calculated as $SPfinal = Y \times (1 - 0.20)$, which simplifies to $SPfinal} = 0.80Y$.
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 $₹100$.
- Calculate the Initial Selling Price ($X$): Given a $25%$ profit margin: $X = 100 \times (1 + 0.25) = ₹125$.
- Define the Festive Sale Final Selling Price ($SPfinal$): The price after a $20%$ discount on the marked price $Y$ is: $SP_{final} = Y \times (1 - 0.20) = 0.80Y$.
- Determine the required $SPfinal$ for a $60%$ Profit: For the festive sale, if the profit is $60%$, the final selling price must be: $SP_{final} = CP \times (1 + \text{Target Profit Rate}) = 100 \times (1 + 0.60) = ₹160$.
- Calculate the Marked Price ($Y$): By equating the expressions for $SPfinal$ 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 $₹125$).
- 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: $\text{Percentage Profit} = \frac{\text{Profit}}{CP} \times 100\% = \frac{60}{100} \times 100\% = 60\%$.
Similar Questions
By selling a bag at Rs. 230, profit of 15% is made. The selling price of the bag, when it is sold at 20% profit would be
A trader had 630 kgs of rice. He sold a part of it at 15% profit and the rest at 8% profit, so that he made a total profit of 12%. How much rice (in kgs) did he sell at 8% profit?
The value of (sin A + cosec A)² + (cos A + sec A)² is:
The following pie chart below shows the expenditure in book publishing by a publisher under various heads.
Given that marked price of a book is ₹270, what is the cost of paper to publish a single copy of the book if the marked price of a book is 20% more than its cost price?
Loss of 20% on selling price is equal to x% loss in cost price. What is x?
A shopkeeper marks his goods 50% more than the cost price and allows a discount of 25%. His profit or loss percentage is:
The selling price of 6 bananas is equal to the cost price of 8 bananas. Then the percentage of profit is
A merchant buys 25 litres of milk daily at the rate of ₹ 12 per litre. He mixes 5 litres of water in it and sells at the rate ₹ 10.40 per litre. His gain/loss is:
If the ratio of cost price and selling price be 10:11, then the profit percentage is
If 10% loss is made on selling price, then the rate of loss on the cost price will be:
Important Questions from Profit and Loss
- Veer bought some sharpeners at the rate of ₹180/dozen. He sold them for ₹23 each. His profit percentage is ____ % (rounded off to two decimal places).
- A shopkeeper lists the price of a fan at 60% above its cost price and offers a 15% discount on its list price. If he earns a profit of ₹117, then what is the list price (in ₹) of the fan?
- The marked price of an article is ₹800. It is sold at two successive discounts of 24% and 15%, respectively. Find the selling price of the article.
- A discount of 13% on the marked price of an article is allowed and then the article is sold for ₹348. The marked price of the article is:
- A trader claims to sell grains at a profit of 29%, but also dishonestly uses a weight which is 13% less than what is mentioned on it. Find the total percentage of profit earned by the trader. (Round off the answer to the nearest whole number.)
