93.5%
Calculating Profit Percentage on Articles with Discounts
This solution details the calculation for finding the profit percentage on article Y, using the given information about article X's sale.
Step 1: Determine the Marked Price (MP) using Article X's Data
The dealer purchases article X for a Cost Price (CP) of ₹2,000. It is sold after applying two successive discounts (28% and 90%), resulting in a Profit of ₹322.
- First, calculate the Selling Price (SP) of article X: SP = CP + Profit = ₹2,000 + ₹322 = ₹2,322.
- Assume the Marked Price (MP) is P. The SP after successive discounts is: SP = $P \times (1 - \frac{28}{100}) \times (1 - \frac{90}{100})$ SP = $P \times (1 - 0.28) \times (1 - 0.90)$ SP = $P \times 0.72 \times 0.10$ SP = $0.072 \times P$
- Now, equate the calculated SP with the actual SP to find the MP (P): $0.072 \times P = 2322$ $P = \frac{2322}{0.072} = \frac{2322000}{72} = 32250$
Thus, the Marked Price (MP) for both articles is ₹32,250.
Step 2: Calculate the Selling Price (SP) of Article Y
Article Y has the same CP of ₹2,000 and MP of ₹32,250. It is sold with a single discount of 88%.
- Calculate the SP of article Y: SP = $MP \times (1 - \frac{\text{Discount Percentage}}{100})$ SP = $32250 \times (1 - \frac{88}{100})$ SP = $32250 \times (1 - 0.88)$ SP = $32250 \times 0.12$ SP = $3870$
The Selling Price (SP) of article Y is ₹3,870.
Step 3: Calculate the Profit Percentage on Article Y
Determine the Profit made on article Y:
- Profit = SP of Y - CP of Y Profit = ₹3,870 - ₹2,000 = ₹1,870
Finally, calculate the Profit Percentage:
- Profit Percentage = $(\frac{\text{Profit}}{CP}) \times 100$ Profit Percentage = $(\frac{1870}{2000}) \times 100$ Profit Percentage = $0.935 \times 100$ Profit Percentage = $93.5\%$
The calculated profit percentage on article Y is 93.5%.
Important Questions from Profit and Loss
By selling an article for Rs. 2,200, a profit of 10% is earned. If the same article is sold for Rs. 2,600, then what will be the gain percentage?
By selling an article for Rs. 640, a person loses 15% of its selling price. At what price (in Rs.) should he sell it to gain 15% on its cost price?
The selling prices of articles A and B are the same. A is sold at a profit of 28 percent and B is sold at a loss of 24 percent. If the total selling price of the both articles is Rs. 48640, then what is the cost price of A and B, respectively ?
The cost price of an article is Rs. 2800. Profit as a percentage of selling price is 20 percent. What is the actual profit (in Rs.) ?
A trader bought 640 kg of rice. He sold a part of rice at 20% profit and the rest at 5% loss. He earned a profit of 15% in the entire transaction. What is the quantity (in kg) of rice that he sold at 5% loss?
