Cost price of two motorcycles is same. One is sold at a profit of `15%` and the other for ₹ 4800 more than the first. If the net profit is `20%`. Find the cost price of each motorcycle:

Options

A. ₹ 48000
B. ₹ 52000
C. ₹ 36000
D. ₹ 42500

Answer

To solve the problem step by step, we will denote the cost price of each motorcycle as \( CP \).

### Step 1: Calculate the selling price of the first motorcycle.
The first motorcycle is sold at a profit of 15%. Therefore, the selling price (SP1) of the first motorcycle can be calculated as:
\[ SP_1 = CP + (15\% \text{ of } CP) = CP + 0.15 \times CP = 1.15 \times CP \]

### Step 2: Calculate the selling price of the second motorcycle.
The second motorcycle is sold for ₹4800 more than the first motorcycle. Thus, the selling price (SP2) of the second motorcycle can be expressed as:
\[ SP_2 = SP_1 + 4800 = 1.15 \times CP + 4800 \]

### Step 3: Calculate the net selling price based on the overall profit.
The net profit from both motorcycles is 20%. Therefore, the total selling price for both motorcycles combined can be expressed as:
\[ \text{Total SP} = 2 \times CP + (20\% \text{ of } 2 \times CP) = 2 \times CP + 0.20 \times (2 \times CP) = 2 \times CP + 0.4 \times CP = 2.4 \times CP \]

### Step 4: Set up the equation for total selling price.
The total selling price is also equal to the sum of the selling prices of both motorcycles:
\[ SP_1 + SP_2 = 1.15 \times CP + (1.15 \times CP + 4800) = 2.3 \times CP + 4800 \]

### Step 5: Equate the two expressions for total selling price.
Now we can set the two expressions for total selling price equal to each other:
\[ 2.4 \times CP = 2.3 \times CP + 4800 \]

### Step 6: Solve for the cost price (CP).
Subtract \( 2.3 \times CP \) from both sides:
\[ 2.4 \times CP - 2.3 \times CP = 4800 \]
\[ 0.1 \times CP = 4800 \]
Now, divide both sides by 0.1:
\[ CP = \frac{4800}{0.1} = 48000 \]

### Step 7: Conclusion
The cost price of each motorcycle is ₹48000.