Mr Dev sold a bus for Rs. 2210 with a loss of 15%. At what price should the bus be sold to get a profit of 15% ?

Options

A. Rs. 2980
B. Rs. 3000
C. Rs. 2970
D. Rs. 2990

Answer

To solve the problem step-by-step, we will first determine the cost price of the bus based on the selling price at a loss, and then calculate the selling price needed to achieve a profit.

### Step 1: Determine the Cost Price (CP)
Given that Mr. Dev sold the bus for Rs. 2210 at a loss of 15%, we can express this mathematically.

Let the Cost Price (CP) be represented as \( x \).

When there is a loss of 15%, the Selling Price (SP) is given by:
\[ SP = CP - (Loss \% \times CP) = CP \times (1 - \frac{Loss \%}{100}) \]
Substituting the values we have:
\[ 2210 = x \times (1 - 0.15) = x \times 0.85 \]

### Step 2: Solve for Cost Price (CP)
To find \( x \):
\[ x = \frac{2210}{0.85} \]
Calculating this gives:
\[ x = 2600 \]

### Step 3: Calculate Selling Price for a Profit of 15%
Now, we need to find the selling price at a profit of 15%. The Selling Price (SP) when there is a profit is given by:
\[ SP = CP + (Profit \% \times CP) = CP \times (1 + \frac{Profit \%}{100}) \]
Substituting the values we have:
\[ SP = 2600 \times (1 + 0.15) = 2600 \times 1.15 \]

### Step 4: Calculate the Selling Price
Now, calculating this gives:
\[ SP = 2990 \]

### Conclusion
Thus, the bus should be sold for Rs. 2990 to achieve a profit of 15%.