Jasmine allows 4% discount on the marked price of her goods and still earns a profit of 20%. What is the cost price of a shirt if its marked price is Rs 850?
जैस्मिन अपनी वस्तुओं के अंकित मूल्य पर 4% छूट देती है और फिर भी 20% लाभ अर्जित करती है। उस कमीज की लागत क्या है । जिसका अंकित मूल्य र 850 है?

Options

A. Rs 700
B. Rs 680
C. Rs 650
D. Rs 720

Explanation

To find the cost price of the shirt given the marked price and the discounts, we can follow these steps:

### Step 1: Calculate the Selling Price after Discount
The marked price (MP) of the shirt is Rs 850. Jasmine allows a discount of 4%.

To find the selling price (SP) after the discount, we can use the formula:
\[ \text{SP} = \text{MP} - \text{Discount} \]
The discount can be calculated as:
\[ \text{Discount} = \frac{4}{100} \times \text{MP} = \frac{4}{100} \times 850 = 34 \]
So, the selling price will be:
\[ \text{SP} = 850 - 34 = 816 \]

### Step 2: Relate Selling Price to Cost Price
We know that Jasmine earns a profit of 20%. This means:
\[ \text{SP} = \text{CP} + \text{Profit} \]
Where profit can be expressed in terms of cost price (CP):
\[ \text{Profit} = \frac{20}{100} \times \text{CP} = \frac{1}{5} \times \text{CP} \]
Thus, we can rewrite the selling price as:
\[ \text{SP} = \text{CP} + \frac{1}{5} \times \text{CP} = \frac{6}{5} \times \text{CP} \]

### Step 3: Solve for Cost Price
Now we can set the selling price equal to the expression we found:
\[ 816 = \frac{6}{5} \times \text{CP} \]
To find the cost price, we can rearrange this equation:
\[ \text{CP} = \frac{5}{6} \times 816 \]
Calculating this gives:
\[ \text{CP} = \frac{5 \times 816}{6} = \frac{4080}{6} = 680 \]

### Final Answer
The cost price of the shirt is Rs 680.

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