A dealer offers a discount of 10% on the marked price of an article and still makes a profit of 20%. If its marked price is Rs. 800, then the cost price of the article is:

Options

A. Rs. 900
B. Rs. 800
C. Rs. 700
D. Rs. 600

Answer

To find the cost price of the article, we can follow these steps:

### Step 1: Determine the Selling Price
The marked price (MP) of the article is given as Rs. 800. The dealer offers a discount of 10% on this marked price.

\[ \text{Discount} = 10\% \text{ of } 800 = \frac{10}{100} \times 800 = 80 \]

Now, we can calculate the selling price (SP) after the discount:

\[ \text{Selling Price (SP)} = \text{Marked Price (MP)} - \text{Discount} \]

\[ \text{SP} = 800 - 80 = 720 \]

### Step 2: Relate Selling Price to Cost Price
We know that the dealer makes a profit of 20%. This means that the selling price is 120% of the cost price (CP).

Let’s denote the cost price as CP. Therefore, we can write:

\[ \text{SP} = 120\% \text{ of CP} \]

This can be expressed mathematically as:

\[ \text{SP} = \frac{120}{100} \times \text{CP} = 1.2 \times \text{CP} \]

### Step 3: Solve for Cost Price
Now, we can set the selling price equal to the expression we derived:

\[ 720 = 1.2 \times \text{CP} \]

To find CP, we can rearrange the equation:

\[ \text{CP} = \frac{720}{1.2} \]

Calculating this gives:

\[ \text{CP} = 600 \]

### Conclusion
Thus, the cost price of the article is Rs. 600.

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