A person sold a chair at a profit of `13%`. Had he sold it for Rs. 607.50 more, he would have gained `x%` If the cost price of the chair is Rs. 3750, then the value of x is:

Options

A. 30
B. 32
C. `28.4`
D. `29.2`

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the given data
- Cost Price (CP) of the chair = Rs. 3750
- Profit Percentage when sold = 13%
- Additional amount if sold = Rs. 607.50

### Step 2: Calculate the Selling Price (SP) at 13% profit
To find the Selling Price (SP) when sold at a profit of 13%, we use the formula:
\[ SP = CP + (Profit \% \times CP) \]
Substituting the values:
\[ SP = 3750 + (13\% \times 3750) \]
Calculating the profit:
\[ 13\% \text{ of } 3750 = \frac{13}{100} \times 3750 = 487.5 \]
Now, calculate SP:
\[ SP = 3750 + 487.5 = 4237.5 \]

### Step 3: Calculate the new Selling Price with the additional amount
If he sold it for Rs. 607.50 more, the new Selling Price (SP') would be:
\[ SP' = SP + 607.5 = 4237.5 + 607.5 = 4845 \]

### Step 4: Calculate the new profit percentage (x%)
Now, we need to find the new profit percentage (x%) when the Selling Price is Rs. 4845. The profit can be calculated as:
\[ \text{Profit} = SP' - CP = 4845 - 3750 = 1095 \]
Now, we can find the profit percentage (x%):
\[ x\% = \left(\frac{\text{Profit}}{CP}\right) \times 100 = \left(\frac{1095}{3750}\right) \times 100 \]
Calculating:
\[ x\% = \left(\frac{1095}{3750}\right) \times 100 \approx 29.2\% \]

### Conclusion
The value of x is approximately **29.2%**.

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