Raheem sells a machine for Rs 48 lakhs at a loss. If instead he had sold it for Rs 60 lakhs, his gain would have been five times the former loss. What is the cost price of the machine in lakhs of rupees?

Introduction / Context:
This question is structurally similar to earlier profit and loss problems where a single cost price is linked to two different selling prices, one giving a loss and another giving a gain. The relation that the gain is a multiple of the loss allows us to write an algebraic equation and determine the cost price.

Given Data / Assumptions:

• First selling price SP1 = Rs 48 lakhs, giving a loss.
• Second selling price SP2 = Rs 60 lakhs, giving a gain.
• The gain at Rs 60 lakhs is five times the loss at Rs 48 lakhs.
• The cost price CP is the same in both cases.
• Required: CP in lakhs of rupees.

Concept / Approach:
When SP is less than CP, loss = CP - SP. When SP is greater than CP, gain = SP - CP. Let the loss at SP1 be L. Then L = CP - 48. The gain at SP2 is 60 - CP and is given to be 5L. Using the equation 60 - CP = 5 * (CP - 48), we can solve for CP directly.

Step-by-Step Solution:
Let CP = x lakhs. Loss at SP1 = x - 48. Gain at SP2 = 60 - x. Given 60 - x = 5(x - 48). Expand: 60 - x = 5x - 240. Rearrange: 60 + 240 = 5x + x → 300 = 6x. So x = 300 / 6 = 50 lakhs.

Verification / Alternative check:
With CP = 50 lakhs, loss at 48 lakhs is 50 - 48 = 2 lakhs. Gain at 60 lakhs is 60 - 50 = 10 lakhs. Here gain is exactly five times the loss (10 = 5 * 2), which matches the condition. Therefore CP = 50 lakhs is consistent with both selling prices.

Why Other Options Are Wrong:
If CP were 58 or 69.6 or 42 lakhs, then the loss at 48 lakhs and gain at 60 lakhs would not satisfy the exact 5 times relation. Quick substitution shows that the ratio of gain to loss would be different from five in those cases.

Common Pitfalls:
A typical mistake is misinterpreting the sentence and writing the equation with loss equal to five times gain instead of the other way around. Another common error is to treat the given values as profit percentages, when in fact the question uses absolute rupee amounts for gain and loss.

Final Answer:
The cost price of the machine is Rs 50 lakhs.