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 ?

Options

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

Answer

To find the cost price of the shirt when the marked price is Rs 850 and a 4% discount is given while still earning a profit of 20%, we can follow these steps:

### Step 1: Identify the given values
- Marked Price (MP) = Rs 850
- Discount = 4%
- Profit = 20%

### Step 2: Calculate the effective selling price (SP) after the discount
The selling price after the discount can be calculated using the formula:
\[ \text{SP} = \text{MP} - \text{Discount} \]

First, we calculate the amount of the discount:
\[ \text{Discount Amount} = \frac{4}{100} \times \text{MP} = \frac{4}{100} \times 850 = 34 \]

Now, we can find the selling price:
\[ \text{SP} = \text{MP} - \text{Discount Amount} = 850 - 34 = 816 \]

### Step 3: Relate Selling Price to Cost Price using Profit
We know that:
\[ \text{SP} = \text{CP} + \text{Profit} \]

The profit can be expressed as:
\[ \text{Profit} = \frac{20}{100} \times \text{CP} = 0.2 \times \text{CP} \]

Thus, we can write:
\[ \text{SP} = \text{CP} + 0.2 \times \text{CP} = 1.2 \times \text{CP} \]

### Step 4: Set up the equation
From the above relationship, we can set up the equation:
\[ 816 = 1.2 \times \text{CP} \]

### Step 5: Solve for Cost Price (CP)
To find the cost price, we rearrange the equation:
\[ \text{CP} = \frac{816}{1.2} \]

Calculating this gives:
\[ \text{CP} = 680 \]

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

---