The cost price of article A and selling price of article B is Rs. 200 and Rs. 240 respectively. Article A was sold at 2x% profit while article B was sold at x% profit. Find the sum of selling price of both articles if the ratio of selling price of article A to the cost price of article B is 7:5 .

To solve this problem, we will use the given information and apply basic algebra to find the required selling prices and their sum. Let's denote the cost price (CP) and selling price (SP) of articles A and B as follows:

- \( \text{CP of article A} = Rs. 200 \)
- \( \text{SP of article B} = Rs. 240 \)
- \( \text{Profit percentage on article A} = 2x\% \)
- \( \text{Profit percentage on article B} = x\% \)

We are also given that the ratio of the selling price of article A to the cost price of article B is 7:5. Let's denote the cost price of article B as \( CP_B \).

### Step 1: Express Selling Price of Article A
The selling price of article A (\( SP_A \)) can be expressed in terms of its cost price and profit percentage as follows:
\[
SP_A = 200 \left(1 + \frac{2x}{100}\right) = 200 \left(1 + \frac{x}{50}\right) = 200 + \frac{200x}{50} = 200 + 4x
\]

### Step 2: Express Selling Price of Article B
The selling price of article B (\( SP_B \)) can be expressed in terms of its cost price and profit percentage as follows:
\[
SP_B = CP_B \left(1 + \frac{x}{100}\right)
\]

Given that \( SP_B = 240 \), we can write:
\[
240 = CP

Learn how to solve a profit and loss problem involving two articles, where the selling price of Article A and the cost price of Article B are given in a specific ratio. Includes step-by-step calculations and explanations. Suitable for Grades 9-12.

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