The cost price of article A is equal to the selling price of article B. Article A is sold at a profit of $33\frac{1}{3}\%$, and article B is sold at a profit of $50\%$. If the sum of the cost price of article B and the selling price of article A is Rs. 672, what is the cost price of article A?

Question

Accepted Answer

**Solution:**

1. Let the cost price of article A be $x$. Given that the cost price of article A equals the selling price of article B, so:
   - Selling price of article B = $x$

2. Article A is sold at a profit of $33\frac{1}{3}\%$, which is $\frac{1}{3}$ or $33.33\%$ profit.
   - Selling price of article A = $x + \frac{1}{3}x = \frac{4}{3}x$

3. Article B is sold at a profit of $50\%$.
   - Let the cost price of article B be $y$.
   - Selling price of article B = $y + 0.5y = 1.5y$

4. From step 1, selling price of article B = $x$, so:
   $$1.5y = x \implies y = \frac{x}{1.5} = \frac{2x}{3}$$

5. Given that the sum of the cost price of article B and the selling price of article A is Rs. 672:
   $$y + \frac{4}{3}x = 672$$

6. Substitute $y = \frac{2x}{3}$:
   $$\frac{2x}{3} + \frac{4x}{3} = 672$$

7. Combine terms:
   $$\frac{2x + 4x}{3} = 672 \implies \frac{6x}{3} = 672 \implies 2x = 672$$

8. Solve for $x$:
   $$x = \frac{672}{2} = 336$$

**Answer:** Rs. 336

Answer

Answer

Answer

Answer