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We are given a situation where the seller is using a faulty weighing machine. Initially, with a faulty machine, the seller makes a 15% profit. The faulty machine shows 1000 gm when it is actually 950 gm. After the machine is corrected to show the actual 1000 gm, we are tasked with finding what the new selling price should be to maintain the same percentage profit.

Let's break it down step-by-step:

### Given Data:
- The seller makes **15% profit** on the cost price \( x \) when using the faulty machine.
- The faulty machine shows 1000 gm of rice when the actual quantity is 950 gm.
- Now, the machine is corrected, and it shows the actual 1000 gm.
  
We need to find the new selling price to maintain the same **15% profit**.

### Step 1: Initial Selling Price with Faulty Machine
- When the machine shows 1000 gm, the seller is actually giving only 950 gm.
- Since the seller is making a 15% profit, the **selling price** when using the faulty machine is:
  
  \[
  \text{Selling Price} = \text{Cost Price} + 15\% \text{Profit} = 1.15x
  \]

  But this selling price corresponds to 950 gm, not 1000 gm.

### Step 2: Adjust Selling Price for Correct Machine
- With the corrected machine, the seller will now give 1000 gm of rice.
- To maintain the same profit margin, the new selling price for 1000 gm should be proportional to the selling price for 950 gm. So, we can set up the ratio:

  \[
  \frac{\text{New Selling Price}}{1.15x} = \frac{1000}{950}
  \]

### Step 3: Solve for New Selling Price
- Rearranging the equation to solve for the new selling price:

  \[
  \text{New Selling Price} = 1.15x \times \frac{1000}{950} = 1.15x \times \frac{20}{19}
  \]

  Simplifying this expression:

  \[
  \text{New Selling Price} = 1.15x \times 1.05263 = 1.2105x
  \]

Thus, the new selling price should be approximately **1.2105x** to maintain the same 15% profit after the machine is corrected.

However, this is not one of the options provided in the question. Let's check if there's any adjustment needed to match the choices or if there is a misunderstanding in interpreting the faulty machine setup.

The answer closest to **1.2105x** is not listed, but it indicates that there might be an issue with the options provided.

Let me know if you'd like to dive deeper into the discrepancy or explore this problem further!

Here are 5 related questions:
1. What would the selling price be if the cost price increased by 10%?
2. How does the error in weighing affect the actual profit percentage?
3. How can we model the relationship between profit percentage and faulty machine errors?
4. What if the faulty machine showed 1000 gm but delivered 1050 gm instead?
5. How would the profit margin change if the cost price doubled?

**Tip:** In problems involving percentages and ratios, always verify whether given values are proportional or need adjustments, especially when multiple factors are involved like faulty equipment.

The cost price and selling price of rice are the same. Due to a faulty weighing machine, the seller earns a 15% profit. If Rs. x is the cost price of 1000 gm rice and the machine is changed which shows 1000 gm instead of 950 gm, what should be the selling price (in Rs.) now to get the same percentage of profit?

In this problem, the seller previously earned a 15% profit due to a faulty weighing machine, which displayed 1000 gm but delivered only 950 gm of rice. After the machine is corrected, learn how to calculate the new selling price that maintains the same 15% profit margin. This solution involves ratios, proportions, and basic profit calculation.

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