Ram Kumar sold his motor cycle to Mohan at a loss of 28%. Mohan spent 1680 on its repairs and sold the motor cycle to Sohan for . 35910, thereby, making a profit of 12.5%. Find the cost of the motor cycle for Ram Kumar.

Options

A. 38000
B. 35000
C. 40000
D. 42000

Answer

To find the cost of the motorcycle for Ram Kumar, we can follow these steps:

### Step 1: Define Variables
Let the cost price of the motorcycle for Ram Kumar be \( x \).

### Step 2: Calculate Selling Price for Ram Kumar
Since Ram Kumar sold the motorcycle to Mohan at a loss of 28%, we can calculate the selling price (SP) for Ram Kumar:
\[ \text{SP} = x - 0.28x = 0.72x \]

### Step 3: Calculate Total Cost Price for Mohan
Mohan spent ₹1680 on repairs after buying the motorcycle. Therefore, Mohan's total cost price (CP) is:
\[ \text{CP}_{\text{Mohan}} = \text{SP}_{\text{Ram}} + \text{Repairs} = 0.72x + 1680 \]

### Step 4: Calculate Selling Price for Mohan
Mohan sold the motorcycle to Sohan for ₹35910, making a profit of 12.5%. We can express this profit as a fraction:
\[ \text{Profit} = 12.5\% = \frac{1}{8} \]
Thus, the selling price (SP) can be expressed in terms of Mohan's cost price:
\[ \text{SP}_{\text{Mohan}} = \text{CP}_{\text{Mohan}} \times \left(1 + \frac{1}{8}\right) = \text{CP}_{\text{Mohan}} \times \frac{9}{8} \]

### Step 5: Set Up the Equation
Now we can set up the equation based on the selling price:
\[ 35910 = \left(0.72x + 1680\right) \times \frac{9}{8} \]

### Step 6: Solve for \( x \)
Multiply both sides by 8 to eliminate the fraction:
\[ 8 \times 35910 = 9(0.72x + 1680) \]
\[ 287280 = 9(0.72x + 1680) \]
Now divide both sides by 9:
\[ \frac{287280}{9} = 0.72x + 1680 \]
Calculating the left side:
\[ 31920 = 0.72x + 1680 \]
Now, subtract 1680 from both sides:
\[ 31920 - 1680 = 0.72x \]
\[ 30240 = 0.72x \]
Finally, divide by 0.72 to find \( x \):
\[ x = \frac{30240}{0.72} = 42000 \]

### Conclusion
The cost of the motorcycle for Ram Kumar is **₹42000**.

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