Calculating Profit Percentage on Article Y
This problem involves calculating the profit percentage for an article (Y) after understanding the pricing and discounts applied to another article (X) from the same dealer. We are given the cost price (CP) for both articles, details about discounts on X, the profit made on X, and the discount on Y. The goal is to find the profit percentage on Y.
Understanding the Given Information
- Cost Price (CP) of Article X = ₹2,000
- Cost Price (CP) of Article Y = ₹2,000
- Both articles are marked at the same Marked Price (MP). Let this be $M$.
- Article X is sold with two successive discounts: 44% and 37%.
- Profit earned on Article X = ₹989.
- Article Y is sold with a single discount of 64%.
Step 1: Calculate the Selling Price (SP) of Article X
The profit is the difference between the selling price and the cost price. We know the CP of X and the profit earned on X.
Profit = Selling Price (SPX) - Cost Price (CPX)
Given Profit on X = ₹989 and CPX = ₹2,000.
SPX = CPX + Profit on X
SPX = ₹2,000 + ₹989 = ₹2,989
Step 2: Determine the Marked Price (MP)
Article X was sold after applying two successive discounts of 44% and 37% on its Marked Price (M). The selling price is calculated as:
SPX = M \times (1 - \text{Discount}_1) \times (1 - \text{Discount}_2)
SPX = M \times (1 - 0.44) \times (1 - 0.37)
SPX = M \times (0.56) \times (0.63)
SPX = M \times 0.3528
We know SPX = ₹2,989. So, we can find M:
₹2,989 = M \times 0.3528
M = \frac{₹2,989}{0.3528}
M \approx ₹8,472.22
Since both articles are marked at the same price, the Marked Price for Article Y is also approximately ₹8,472.22.
Step 3: Calculate the Selling Price (SP) of Article Y
Article Y is sold at a single discount of 64% on its Marked Price (M).
SPY = M \times (1 - \text{Discount})
SPY = M \times (1 - 0.64)
SPY = M \times 0.36
Using the value of M calculated above:
SPY = \left( \frac{₹2,989}{0.3528} \right) \times 0.36
SPY = ₹2,989 \times \frac{0.36}{0.3528}
SPY = ₹2,989 \times \frac{3600}{3528}
SPY = ₹2,989 \times \frac{100}{98}
SPY = ₹2,989 \times \frac{50}{49}
SPY = \frac{₹149,450}{49} \approx ₹3,050.00
Step 4: Calculate the Profit on Article Y
The profit on Article Y is the difference between its selling price and cost price.
ProfitY = SPY - CPY
ProfitY = ₹3,050.00 - ₹2,000
ProfitY = ₹1,050.00
Step 5: Calculate the Profit Percentage on Article Y
The profit percentage is calculated with respect to the cost price.
Profit PercentageY = \left( \frac{\text{Profit}_Y}{\text{CP}_Y} \right) \times 100
Profit PercentageY = \left( \frac{₹1,050.00}{₹2,000} \right) \times 100
Profit PercentageY = 0.525 \times 100
Profit PercentageY = 52.50%
Therefore, the profit percentage on Article Y is 52.50%.
Important Questions from Profit & Loss
- I bought two bicycles for ₹1,200. I sold the first one at a loss of 13% and the second at a gain of 11%. If, on the whole I made neither a loss nor a gain, find the cost price (in ₹) of the first bicycle.
- A dealer buys two articles X and Y for ₹1,500 each. He marks each of them at the same price. He sells X by giving two successive discounts of 25% and 44% and still earns 279 as profit. If he sells Y at a single discount of 58%, then what is the profit percentage on Y?
The marked price of 55 items was equal to the cost price of 99 items. The selling price of 56 items was equal to the marked price of 35 items. Calculate the profit or loss percentage from the sale of each item.
Raman fixes the sale price of his goods at 16% above the cost price. He sells his goods at 12% less than the fixed price. Find the profit percentage correct to two places of decimal.
- A dishonest dealer professes to sell grains at cost price, but he uses a weight of 925 g for 1 kg weight. Find his gain percentage. (Approximate to two decimals.)
