Mr Ashwani sold a bus for Rs. 510 with a loss of 15 %. At what price should the bus be sold to get a profit of 15 %?

Options

A. Rs.700
B. Rs. 690
C. Rs. 650
D. Rs. 680

Answer

To solve the problem step by step, we will first determine the cost price (CP) of the bus based on the selling price (SP) and the loss percentage. Then, we will calculate the new selling price required to achieve a profit of 15%.

### Step 1: Determine the Cost Price (CP)
Given that the selling price (SP) is Rs. 510 and the loss is 15%, we can use the formula for loss:

\[ SP = CP - \text{Loss} \]

The loss can be expressed as:

\[ \text{Loss} = \frac{15}{100} \times CP \]

Substituting this into the SP formula gives:

\[ 510 = CP - \left(\frac{15}{100} \times CP\right) \]

This simplifies to:

\[ 510 = CP \left(1 - \frac{15}{100}\right) = CP \left(\frac{85}{100}\right) \]

Now, we can solve for CP:

\[ CP = \frac{510 \times 100}{85} \]

Calculating this gives:

\[ CP = \frac{51000}{85} = 600 \]

### Step 2: Calculate the Selling Price for a Profit of 15%
Now that we have the cost price (CP) as Rs. 600, we can calculate the new selling price (SP) required for a profit of 15%. The formula for profit is:

\[ SP = CP + \text{Profit} \]

The profit can be expressed as:

\[ \text{Profit} = \frac{15}{100} \times CP \]

Substituting this into the SP formula gives:

\[ SP = CP + \left(\frac{15}{100} \times CP\right) \]

This simplifies to:

\[ SP = CP \left(1 + \frac{15}{100}\right) = CP \left(\frac{115}{100}\right) \]

Substituting the CP value:

\[ SP = 600 \times \frac{115}{100} \]

Calculating this gives:

\[ SP = 600 \times 1.15 = 690 \]

### Final Answer
The bus should be sold for Rs. 690 to achieve a profit of 15%.

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