Solution Explanation: Profit Percentage Calculation
This problem involves calculating the profit percentage on an article (Y) after understanding the pricing and discount structure of two articles (X and Y) sold by a dealer.
Understanding the Problem Details
- The dealer buys two articles, X and Y, at the same Cost Price (CP).
- CP for each article = ₹1,500.
- Both articles are marked at the same Marked Price (MP).
- Article X is sold with two successive discounts: 25% and 44%.
- The profit earned on selling Article X is ₹279.
- Article Y is sold with a single discount of 58%.
- The goal is to find the Profit Percentage on Article Y.
Calculations for Article X
First, let's determine the Selling Price (SP) of Article X and then its Marked Price (MP).
Calculating the Selling Price (SP) of Article X
The Cost Price (CP) of Article X is ₹1,500.
The profit earned on Article X is ₹279.
The Selling Price (SP) is calculated as: $ SP = CP + \text{Profit} $ $ SP_X = ₹1,500 + ₹279 = ₹1,779 $
Calculating the Marked Price (MP) of Article X
Article X was sold after two successive discounts of 25% and 44%. Let the Marked Price be '$M$'.
The price after the first discount (25%) is: $ M \times (1 - 0.25) = M \times 0.75 $
The price after the second discount (44%) is: $ (M \times 0.75) \times (1 - 0.44) = M \times 0.75 \times 0.56 $
This final price is the Selling Price ($SP_X$). So, $ SP_X = M \times 0.75 \times 0.56 $ $ SP_X = M \times 0.42 $
We already calculated $SP_X = ₹1,779$. Therefore, $ ₹1,779 = M \times 0.42 $ $ M = \frac{₹1,779}{0.42} $
Since both articles are marked at the same price, the Marked Price (MP) for Article Y is also $ M = \frac{₹1,779}{0.42} $. Note that we don't need the exact value of M for the next step.
Calculations for Article Y
Now, let's calculate the Selling Price (SP) and Profit Percentage for Article Y.
Calculating the Selling Price (SP) of Article Y
The Cost Price (CP) of Article Y is ₹1,500.
The Marked Price (MP) of Article Y is the same as Article X: $ M = \frac{₹1,779}{0.42} $.
Article Y is sold at a single discount of 58%. The Selling Price ($SP_Y$) is: $ SP_Y = MP \times (1 - \text{Discount Rate}) $ $ SP_Y = M \times (1 - 0.58) $ $ SP_Y = M \times 0.42 $
Substitute the value of MP: $ SP_Y = \left( \frac{₹1,779}{0.42} \right) \times 0.42 $ $ SP_Y = ₹1,779 $
Interestingly, the selling price of Article Y is the same as the selling price of Article X.
Calculating the Profit on Article Y
The Profit on Article Y is calculated as:
$ \text{Profit}_Y = SP_Y - CP_Y $ $ \text{Profit}_Y = ₹1,779 - ₹1,500 = ₹279 $Calculating the Profit Percentage on Article Y
The Profit Percentage is calculated based on the Cost Price:
$ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100\% $ $ \text{Profit Percentage}_Y = \left( \frac{₹279}{₹1,500} \right) \times 100\% $ $ \text{Profit Percentage}_Y = \left( \frac{279}{15} \right) \% $ $ \text{Profit Percentage}_Y = 18.6\% $So, the profit percentage on Article Y is 18.60%.
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 ₹2,000 each. He marks each of them at the same price. He sells X by giving two successive discounts of 44% and 37% and still earns ₹989 as profit. If he sells Y at a single discount of 64%, 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.)
