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%.