What price should Neha mark on a sari which cost her Rs. 3000, so as to gain 20% after allowing a discount of 10%?

Answer

To solve the problem step by step, we will determine the marked price that Neha should set on the sari to achieve a 20% profit after allowing a 10% discount.

### Step 1: Calculate the Selling Price (SP) for a 20% Profit
The cost price (CP) of the sari is Rs. 3000. To find the selling price that includes a 20% profit, we use the formula:

\[ SP = CP + (20\% \text{ of } CP) = CP \times \left(1 + \frac{20}{100}\right) \]

Calculating this gives:

\[ SP = 3000 \times \left(1 + 0.20\right) = 3000 \times 1.20 = 3600 \]

### Step 2: Set Up the Equation for Marked Price (MP)
Let the marked price be \( X \). The discount given is 10% of the marked price, which can be expressed as:

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

The selling price can also be expressed in terms of the marked price and the discount:

\[ SP = MP - \text{Discount} = X - \frac{X}{10} \]

### Step 3: Simplify the Selling Price Equation
Substituting the value of SP we calculated in Step 1:

\[ 3600 = X - \frac{X}{10} \]

This simplifies to:

\[ 3600 = \frac{10X - X}{10} = \frac{9X}{10} \]

### Step 4: Solve for the Marked Price (MP)
To isolate \( X \), we multiply both sides of the equation by 10:

\[ 3600 \times 10 = 9X \]
\[ 36000 = 9X \]

Now, divide both sides by 9:

\[ X = \frac{36000}{9} = 4000 \]

### Conclusion
The marked price that Neha should set on the sari is Rs. 4000.

---