The profit earned by selling a bucket at an 8% gain is Rs 28 more than the loss incurred when selling it at an 8% loss. What is the cost price (in rupees) of the bucket?

Introduction / Context:
This is a typical profit and loss question that uses symmetric profit and loss percentages on the same cost price. The difference between the numerical profit and loss amounts is given, and we must determine the cost price. Problems like this reinforce the idea that equal percentage profit and loss on the same cost price lead to equal absolute amounts when expressed in terms of the cost price, and the difference between them relates directly to the cost.

Given Data / Assumptions:

• Gain percentage in one case = 8%.
• Loss percentage in the other case = 8%.
• Profit at 8% is larger than the loss at 8% by Rs 28.
• Let the cost price be C rupees.
• We need to find the value of C.

Concept / Approach:
When cost price is C:

• Profit at 8% is 0.08C.
• Loss at 8% is also 0.08C.

The difference between these profit and loss amounts is 0.08C - ( -0.08C ) or simply 0.16C if we consider the distance between them. However, the question directly states that the profit is Rs 28 more than the loss, which equals 0.16C. So we set 0.16C = 28 and solve.

Step-by-Step Solution:
Let cost price of the bucket be C. Profit at 8% = 8% of C = 0.08C. Loss at 8% = 8% of C = 0.08C. Difference between profit and loss is 0.08C + 0.08C = 0.16C. Given that this difference equals Rs 28. So 0.16C = 28. C = 28 / 0.16. C = 175. Therefore, the cost price of the bucket is Rs 175.

Verification / Alternative check:
Check using C = 175:

• Profit at 8% = 0.08 * 175 = 14.
• Loss at 8% = 14 as a numerical amount, but it is a reduction.
• The difference between profit (14) and loss (14) is indeed 14 + 14 = 28 when measured as how much more the profit is than the loss.

This matches the given value of 28, so the cost price is verified as correct.

Why Other Options Are Wrong:
For C = 170, difference = 0.16 * 170 = 27.2, not 28. For C = 190, difference = 30.4. For C = 165, difference = 26.4. For C = 180, difference = 28.8. None of these match the exact difference of 28 stated in the problem.

Common Pitfalls:
Many students mistakenly take 8% of the selling price instead of 8% of the cost price or forget that the difference between profit and loss at the same rate is effectively 16% of cost price. It is also easy to set up the wrong equation if signs are not handled carefully. Always express profit and loss clearly in terms of cost price and then compute the difference.

Final Answer:
The cost price of the bucket is Rs 175.