A businessman earns a profit of 10% by allowing a discount of 10% on the marked price. If the marked price of an article is 77,then find cost price.

Options

A. Rs 63
B. Rs 69.3
C. Rs 69
D. Rs 84

Answer

To find the cost price of the article given the marked price and profit percentage, we can follow these steps:

### Step 1: Understand the Given Information
- Marked Price (MP) = ₹77
- Discount = 10%
- Profit = 10%

### Step 2: Calculate the Selling Price (SP)
Since there is a discount of 10% on the marked price, we can calculate the selling price as follows:

\[ \text{Discount} = \frac{10}{100} \times \text{MP} = \frac{10}{100} \times 77 = 7.7 \]

Now, subtract the discount from the marked price to find the selling price:

\[ \text{SP} = \text{MP} - \text{Discount} = 77 - 7.7 = 69.3 \]

### Step 3: Relate Selling Price to Cost Price
We know that the profit is 10% of the cost price (CP). This means:

\[ \text{SP} = \text{CP} + \text{Profit} \]

Since profit is 10% of CP, we can express it as:

\[ \text{Profit} = \frac{10}{100} \times \text{CP} = \frac{1}{10} \times \text{CP} \]

Thus, we can rewrite the equation for SP:

\[ \text{SP} = \text{CP} + \frac{1}{10} \times \text{CP} = \frac{11}{10} \times \text{CP} \]

### Step 4: Substitute the Selling Price
Now we can substitute the selling price we calculated into the equation:

\[ 69.3 = \frac{11}{10} \times \text{CP} \]

### Step 5: Solve for Cost Price (CP)
To find CP, we can rearrange the equation:

\[ \text{CP} = 69.3 \times \frac{10}{11} \]

Calculating this gives:

\[ \text{CP} = 69.3 \times 0.909090909 = 63 \]

### Conclusion
Thus, the cost price of the article is ₹63.

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