A used car dealer sells a car for Rs. 7.6 lakhs and incurs a loss. If, instead, he had sold the same car for Rs. 9.2 lakhs, his profit would have been three times the amount of his loss. What was the cost price of the car in lakh rupees?

Introduction / Context:
This problem examines the relationship between cost price, selling price, profit and loss. The dealer sells a car at one price and suffers a loss, but at a higher price he would earn a profit that is a multiple of the loss. Using algebra, we can relate these quantities and find the car's cost price in terms of the two given selling prices.

Given Data / Assumptions:

• The car is sold first for Rs. 7.6 lakhs, and this sale results in a loss.
• If it had been sold for Rs. 9.2 lakhs, there would be a profit.
• The profit at Rs. 9.2 lakhs would be three times the loss at Rs. 7.6 lakhs.
• We denote the cost price by x lakh rupees.
• We need to find the value of x.

Concept / Approach:
Let x be the cost price (in lakhs). When the car is sold for less than x, the difference x - 7.6 is the loss. When it is sold for more than x, the difference 9.2 - x is the profit. The key relationship given is that the profit at Rs. 9.2 lakhs is three times the loss at Rs. 7.6 lakhs. This leads to a linear equation in x that we can solve easily.

Step-by-Step Solution:
Let the cost price of the car be x lakh rupees. Loss when sold at Rs. 7.6 lakhs = x - 7.6 (since x is greater than 7.6). Profit when sold at Rs. 9.2 lakhs = 9.2 - x (since 9.2 is greater than x). Given that profit is three times the loss: 9.2 - x = 3 * (x - 7.6). Expand the right-hand side: 9.2 - x = 3x - 22.8. Bring all terms with x to one side: 9.2 + 22.8 = 3x + x. 32 = 4x. Therefore, x = 32 / 4 = 8. So, the cost price of the car is Rs. 8 lakhs.

Verification / Alternative check:
If the cost price is Rs. 8 lakhs, loss at Rs. 7.6 lakhs is 8 - 7.6 = 0.4 lakhs. Profit at Rs. 9.2 lakhs is 9.2 - 8 = 1.2 lakhs. Clearly, 1.2 is exactly three times 0.4, which satisfies the condition that the profit would have been thrice the loss. Hence the value x = 8 is consistent with the problem data.

Why Other Options Are Wrong:
8.50: If cost price were 8.5, loss at 7.6 would be 0.9 and profit at 9.2 would be 0.7, which are not in a 3:1 ratio.
8.75: This gives loss 1.15 and profit 0.45, again violating the condition.
8.25: This gives loss 0.65 and profit 0.95, which do not match the required ratio.
9.00: This would imply loss 1.4 and negative profit at 9.2 (actually a small profit), which clearly does not fit the relationship.

Common Pitfalls:
A common mistake is to reverse the profit and loss expressions or forget that loss is cost price minus selling price while profit is selling price minus cost price. Another typical error is to treat the ratio as profit percentage and loss percentage, instead of using the actual profit and loss amounts. Setting up the simple linear equation correctly from the word statement is crucial for success in this type of question.

Final Answer:
The cost price of the car is Rs. 8 lakhs.