Mr. Piyush sold a bus Rs. 3.400 with a loss of 15%. At what price should the bus sold to get a profit of 15% ?

Options

A. B
B. A
C. D
D. C

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 Mr. Piyush sold the bus for Rs. 3400 at a loss of 15%, we can express this mathematically.

When a loss of 15% occurs, the selling price (SP) is 85% of the cost price (CP).

So, we can write the equation:
\[ SP = CP \times \left(1 - \frac{Loss\%}{100}\right) \]
\[ 3400 = CP \times 0.85 \]

To find the cost price (CP), we rearrange the equation:
\[ CP = \frac{SP}{0.85} \]
\[ CP = \frac{3400}{0.85} \]

### Step 2: Calculate CP

Now we perform the calculation:
\[ CP = \frac{3400 \times 100}{85} \]
\[ CP = \frac{340000}{85} \]
\[ CP = 4000 \]

### Step 3: Determine the Selling Price for a Profit of 15%

Now that we have the cost price (CP) as Rs. 4000, we need to find the selling price (SP) that would give a profit of 15%.

When there is a profit of 15%, the selling price (SP) is 115% of the cost price (CP).

So we can write:
\[ SP = CP \times \left(1 + \frac{Profit\%}{100}\right) \]
\[ SP = 4000 \times 1.15 \]

### Step 4: Calculate the New SP

Now we perform the calculation:
\[ SP = 4000 \times 1.15 \]
\[ SP = 4600 \]

### Final Answer

Thus, the price at which the bus should be sold to achieve a profit of 15% is Rs. 4600.

---