A used two-wheeler dealer sells a scooter for Rs 46,000 and makes some loss. If he had sold it for 58,000 his profit would have been double his loss. What was the cost price (in Rs) of the Scooter?

Options

A. 52000
B. 54000
C. 48000
D. 50000

Answer

To find the cost price (CP) of the scooter, we can set up the problem step by step.

### Step 1: Define the variables
Let the cost price of the scooter be \( CP \).

### Step 2: Understand the selling prices and losses
1. The dealer sells the scooter for Rs 46,000 and incurs a loss. This means:
\[ \text{Loss} = CP - 46000 \]

2. If he had sold it for Rs 58,000, he would have made a profit. This means:
\[ \text{Profit} = 58000 - CP \]

### Step 3: Set up the relationship between profit and loss
According to the problem, the profit when selling for Rs 58,000 is double the loss when selling for Rs 46,000. Therefore, we can write:
\[ 58000 - CP = 2(CP - 46000) \]

### Step 4: Simplify the equation
Expanding the equation gives:
\[ 58000 - CP = 2CP - 92000 \]

### Step 5: Rearranging the equation
Now, let's bring all terms involving \( CP \) to one side:
\[ 58000 + 92000 = 2CP + CP \]
\[ 150000 = 3CP \]

### Step 6: Solve for CP
Now, divide both sides by 3:
\[ CP = \frac{150000}{3} = 50000 \]

### Conclusion
The cost price of the scooter is Rs 50,000.