By selling a sweater for Rs. 750, a shopkeeper gains 25%. For how much should he sell it to gain 30%?

Options

A. 720
B. 780
C. 600
D. 180

Answer

To solve the problem step by step, we will first determine the cost price of the sweater based on the given selling price and profit percentage. Then, we will calculate the new selling price required to achieve a different profit percentage.

### Step 1: Determine the Selling Price and Profit Percentage
The selling price (SP) of the sweater is given as Rs. 750, and the profit percentage is 25%.

### Step 2: Calculate the Cost Price (CP)
To find the cost price, we can use the formula:
\[ \text{Cost Price (CP)} = \frac{\text{Selling Price (SP)} \times 100}{100 + \text{Profit Percentage}} \]
Substituting the values:
\[ \text{CP} = \frac{750 \times 100}{100 + 25} = \frac{750 \times 100}{125} \]
Calculating this gives:
\[ \text{CP} = \frac{75000}{125} = 600 \]
So, the cost price of the sweater is Rs. 600.

### Step 3: Calculate the New Selling Price for 30% Profit
Now, we need to find the selling price that would yield a 30% profit. The profit is calculated on the cost price:
\[ \text{Profit} = \text{CP} \times \frac{\text{Profit Percentage}}{100} = 600 \times \frac{30}{100} = 600 \times 0.3 = 180 \]

### Step 4: Calculate the New Selling Price
The new selling price (SP) can be calculated by adding the profit to the cost price:
\[ \text{New SP} = \text{CP} + \text{Profit} = 600 + 180 = 780 \]

### Final Answer
The shopkeeper should sell the sweater for Rs. 780 to gain a 30% profit.

---