A shopkeeper sold mobiles at Rs 13547 each after giving 8% discount on the Marked price had he not given the discount, he would have earned a profit of 24% on the cost price. what was the cost price of each mobile?

Let the cost price of each mobile be denoted as \( C \), and the marked price be denoted as \( M \).

### Step 1: Setting up the equations

1. **Marked Price and Selling Price Relationship with Discount**:  
   The shopkeeper sold the mobile at Rs 13,547 after giving an 8% discount on the marked price.  
   This gives us the following equation:
   \[
   \text{Selling Price} = M - 0.08M = 0.92M
   \]
   Thus, we can write:
   \[
   0.92M = 13,547
   \]

2. **Marked Price and Cost Price Relationship with Profit**:  
   If the shopkeeper had not given the discount, he would have earned a profit of 24% on the cost price. Therefore, the marked price is related to the cost price as:
   \[
   M = C + 0.24C = 1.24C
   \]
   So:
   \[
   M = 1.24C
   \]

### Step 2: Solving for \( M \) and \( C \)

1. From the first equation, solving for \( M \):
   \[
   M = \frac{13,547}{0.92} = 14,720.65
   \]
   (rounded to 2 decimal places)

2. Now substitute this value of \( M \) into the second equation to find \( C \):
   \[
   1.24C = 14,720.65
   \]
   Solving for \( C \):
   \[
   C = \frac{14,720.65}{1.24} = 11,868.27
   \]
   (rounded to 2 decimal places)

### Final Answer:
The cost price of each mobile is approximately **Rs 11,868.27**.

Would you like a detailed explanation or have any questions?

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Here are 5 questions to expand this concept:

1. How is the selling price calculated with different discount percentages?
2. What would happen to the profit if the discount were increased?
3. How would the calculation change if a different profit percentage was applied?
4. What role does the cost price play in determining the marked price and selling price?
5. How would the problem change if the discount was given after applying taxes?

**Tip:** Always verify whether the percentage profit is based on cost price or marked price, as it impacts the calculations.

A shopkeeper sold mobiles at Rs 13547 each after giving 8% discount on the Marked price had he not given the discount, he would have earned a profit of 24% on the cost price. What was the cost price of each mobile?

Learn how to calculate the cost price of a mobile when a shopkeeper offers a discount of 8% on the marked price and would have earned a 24% profit on the cost price without the discount. This problem covers key concepts in profit and loss and discount calculations, suitable for Grades 9-10.

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