Satish buys two articles type A at Rs 2800 and type B at Rs 8400. He sold type A article at x% profit and mark up type B article 2x% above the cost price and gave x% discount at the time of the sale. By this Satish earn overall (x-6)% profit. Find the value of x.

Options

A. 15
B. 16
C. 25
D. 20

Answer

To solve the problem step by step, we will break down the information given and calculate the required values systematically.

### Step 1: Identify the Cost Prices
- The cost price of article A = Rs. 2800
- The cost price of article B = Rs. 8400

### Step 2: Calculate Selling Price of Article A
- Selling price of article A when sold at x% profit:
\[ \text{Selling Price of A} = \text{Cost Price of A} \times \left(1 + \frac{x}{100}\right) \]
\[ \text{Selling Price of A} = 2800 \times \left(1 + \frac{x}{100}\right) = 2800 + 28x \]

### Step 3: Calculate Mark Price of Article B
- Mark price of article B when marked up by 2x%:
\[ \text{Mark Price of B} = \text{Cost Price of B} \times \left(1 + \frac{2x}{100}\right) \]
\[ \text{Mark Price of B} = 8400 \times \left(1 + \frac{2x}{100}\right) = 8400 + 168x \]

### Step 4: Calculate Selling Price of Article B after Discount
- Selling price of article B after giving x% discount:
\[ \text{Selling Price of B} = \text{Mark Price of B} \times \left(1 - \frac{x}{100}\right) \]
\[ \text{Selling Price of B} = (8400 + 168x) \times \left(1 - \frac{x}{100}\right) \]
\[ = (8400 + 168x) \times \frac{100 - x}{100} \]
\[ = \frac{(8400 + 168x)(100 - x)}{100} \]

### Step 5: Calculate Total Selling Price
- Total Selling Price = Selling Price of A + Selling Price of B
\[ \text{Total Selling Price} = (2800 + 28x) + \frac{(8400 + 168x)(100 - x)}{100} \]

### Step 6: Calculate Total Cost Price
- Total Cost Price = Cost Price of A + Cost Price of B
\[ \text{Total Cost Price} = 2800 + 8400 = 11200 \]

### Step 7: Calculate Overall Profit
- Overall profit is given as (x - 6)% of the total cost price:
\[ \text{Overall Profit} = \frac{(x - 6)}{100} \times 11200 = 112(x - 6) \]

### Step 8: Set Up the Equation
- Profit from selling both articles = Total Selling Price - Total Cost Price
- Set the profit equal to the overall profit:
\[ \text{Selling Price of A} + \text{Selling Price of B} - 11200 = 112(x - 6) \]

### Step 9: Simplify and Solve for x
- Substitute the expressions for Selling Price of A and Selling Price of B into the equation and simplify:
\[ (2800 + 28x) + \frac{(8400 + 168x)(100 - x)}{100} - 11200 = 112(x - 6) \]
- Solve the resulting equation for x.

### Step 10: Final Calculation
- After simplifying, you will find the value of x.

### Conclusion
- The value of x is found to be 20.