Amit brought two cars. He then sold the first car at 10% profit and the second one at 25% profit. The selling price of the second car is 25% more than the selling price of the first car. What is the approximate profit per cent in both the cars together?

Options

A. `17.85%`
B. `18.36%`
C. `16.19%`
D. Cannot be determined

Answer

To solve the problem step by step, let's follow the information given in the question:

### Step 1: Define the Cost Price of the First Car
Let the cost price (CP) of the first car be \( CP_1 = x \).

### Step 2: Calculate the Selling Price of the First Car
The first car is sold at a profit of 10%. Therefore, the selling price (SP) of the first car can be calculated as:
\[ SP_1 = CP_1 + 10\% \text{ of } CP_1 = x + 0.1x = 1.1x \]

### Step 3: Define the Selling Price of the Second Car
According to the problem, the selling price of the second car is 25% more than the selling price of the first car. Therefore:
\[ SP_2 = SP_1 + 25\% \text{ of } SP_1 = SP_1 + 0.25 \times SP_1 = 1.25 \times SP_1 = 1.25 \times 1.1x = 1.375x \]

### Step 4: Define the Cost Price of the Second Car
The second car is sold at a profit of 25%. Let the cost price of the second car be \( CP_2 \). We know that:
\[ SP_2 = CP_2 + 25\% \text{ of } CP_2 = CP_2 + 0.25 \times CP_2 = 1.25 \times CP_2 \]
From the equation above, we can express \( CP_2 \) in terms of \( SP_2 \):
\[ CP_2 = \frac{SP_2}{1.25} = \frac{1.375x}{1.25} = 1.1x \]

### Step 5: Calculate Total Cost Price and Total Selling Price
Now we can find the total cost price and total selling price of both cars:
\[ \text{Total CP} = CP_1 + CP_2 = x + 1.1x = 2.1x \]
\[ \text{Total SP} = SP_1 + SP_2 = 1.1x + 1.375x = 2.475x \]

### Step 6: Calculate Total Profit
The total profit can be calculated as:
\[ \text{Total Profit} = \text{Total SP} - \text{Total CP} = 2.475x - 2.1x = 0.375x \]

### Step 7: Calculate Profit Percentage
The profit percentage can be calculated using the formula:
\[ \text{Profit Percentage} = \left(\frac{\text{Total Profit}}{\text{Total CP}}\right) \times 100 = \left(\frac{0.375x}{2.1x}\right) \times 100 \]
Simplifying this gives:
\[ \text{Profit Percentage} = \left(\frac{0.375}{2.1}\right) \times 100 \approx 17.857\% \]

### Conclusion
The approximate profit percentage in both the cars together is **17.85%**.

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