A used two wheeler dealer sells a scooter for Rs 46,000 and incurs a loss. If instead he had sold it for Rs 58,000, his profit would have been double the amount of his loss in the first sale. What is the cost price of the scooter?

Introduction / Context:
This question links a loss in one selling scenario with a profit in another scenario for the same article. The profit in the second case is given as double the loss in the first case. We must form equations involving cost price and then solve for the unknown cost price. This is a standard algebraic application of profit and loss concepts.

Given Data / Assumptions:
- First selling price S1 = Rs 46,000 with a loss. - Second selling price S2 = Rs 58,000 with a profit. - Profit in the second case is double the loss in the first case. - Cost price of the scooter is the same in both cases.

Concept / Approach:
Let cost price be C. In the first sale, loss L = C - S1. In the second sale, profit P = S2 - C. The condition given is P = 2L. Using these relationships, we set up equations and solve for C. This is a simple system of two equations in two unknowns L and C, which can be solved logically or algebraically.

Step-by-Step Solution:
Step 1: Let cost price = C. Step 2: In the first sale at Rs 46,000, loss L = C - 46,000. Step 3: In the second sale at Rs 58,000, profit P = 58,000 - C. Step 4: Given that profit is double the loss, P = 2L. Step 5: So 58,000 - C = 2 * (C - 46,000). Step 6: Expand the right side: 58,000 - C = 2C - 92,000. Step 7: Bring terms together: 58,000 + 92,000 = 2C + C. Step 8: 150,000 = 3C, so C = 150,000 / 3 = 50,000.

Verification / Alternative check:
Check the loss and profit amounts using C = 50,000. In the first sale, loss L = 50,000 - 46,000 = Rs 4,000. In the second sale, profit P = 58,000 - 50,000 = Rs 8,000. Clearly, P = 2L, since 8,000 is double 4,000. Both conditions of the question are satisfied, confirming that the cost price is correct.

Why Other Options Are Wrong:
If cost price were 52,000, the loss at 46,000 would be 6,000 and profit at 58,000 would be 6,000, not double. If cost price were 54,000 or 48,000, the relationships between profits and losses would also fail when checked. Only C = 50,000 yields a profit exactly twice the loss.

Common Pitfalls:
Students often confuse profit and loss conditions or attempt to average the two selling prices. Another error is to assume that cost price is the mean of 46,000 and 58,000, which would be 52,000, but this ignores the condition that profit is double the loss. Always translate the verbal condition into an equation and then solve systematically.

Final Answer:
The cost price of the scooter is Rs 50,000.