Ratio of Loss incurred by selling an article for Rs 820 and profit gained by selling same article for Rs 950 is 7 : 6. Find the cost price of this article?

Answer

To find the cost price of the article based on the given conditions, we can follow these steps:

### Step 1: Understand the given information
We know that:
- Selling price (SP) for loss = Rs 820
- Selling price (SP) for profit = Rs 950
- Ratio of loss to profit = 7 : 6

### Step 2: Define the loss and profit in terms of a variable
Let the loss incurred when selling for Rs 820 be represented as \( 7x \) and the profit gained when selling for Rs 950 be represented as \( 6x \).

### Step 3: Write equations for selling prices
From the definitions:
- Cost Price (CP) when there is a loss:
\[ CP = SP - \text{Loss} = 820 + 7x \]
- Cost Price (CP) when there is a profit:
\[ CP = SP + \text{Profit} = 950 - 6x \]

### Step 4: Set the two equations for CP equal to each other
Since both expressions represent the same cost price:
\[ 820 + 7x = 950 - 6x \]

### Step 5: Solve for \( x \)
Combine like terms:
\[ 820 + 7x + 6x = 950 \]
\[ 820 + 13x = 950 \]
Subtract 820 from both sides:
\[ 13x = 950 - 820 \]
\[ 13x = 130 \]
Now, divide by 13:
\[ x = \frac{130}{13} = 10 \]

### Step 6: Calculate the loss and profit
Now that we have \( x \):
- Loss = \( 7x = 7 \times 10 = 70 \)
- Profit = \( 6x = 6 \times 10 = 60 \)

### Step 7: Calculate the Cost Price (CP)
Using either equation for CP, we can substitute \( x \):
Using the loss equation:
\[ CP = 820 + 7x = 820 + 70 = 890 \]

### Final Answer
The cost price of the article is Rs 890.

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