An agent receives a commission of 2.5% on the sale of cloth. On a certain day, he earns Rs. 12.50 as commission. What was the total value of cloth sold through him on that day?

Introduction / Context:
This question is a simple application of percentage and commission. The commission percentage and the actual commission amount are given, and we must find the total sales value that produced this commission. Such problems are standard in topics involving brokerage, agency commissions, or sales incentives and help strengthen the link between percentage rates and their corresponding base values.

Given Data / Assumptions:

• The commission rate is 2.5% of the sale value of cloth.
• The agent receives Rs. 12.50 as commission on a particular day.
• We are asked to find the total value of cloth sold through the agent on that day.
• Commission is calculated directly as a percentage of the sales amount with no additional conditions.

Concept / Approach:
The concept is straightforward: commission equals commission rate multiplied by the sales amount. If we let the sales amount be S, then the commission is (2.5/100) * S. Setting this equal to Rs. 12.50 and solving for S gives the sales amount. This is a direct percentage equation where the unknown is the base value corresponding to a known percent of it.

Step-by-Step Solution:
Step 1: Let the total value of cloth sold be S rupees.Step 2: The commission rate is 2.5%, so commission = (2.5/100) * S.Step 3: We are told that the commission amount is Rs. 12.50.Step 4: Set up the equation: (2.5/100) * S = 12.50.Step 5: Rewrite (2.5/100) as 0.025. So 0.025 * S = 12.50.Step 6: Solve for S by dividing both sides by 0.025: S = 12.50 / 0.025.Step 7: 12.50 divided by 0.025 equals 500.Step 8: Therefore, the total value of cloth sold is Rs. 500.

Verification / Alternative check:
We can verify by computing 2.5% of Rs. 500 directly. Calculate 1% of 500, which is 5. Then 2.5% of 500 is 2.5 * 5 = 12.5 rupees. This matches the commission given in the question. The calculation is consistent, and the answer S = 500 is verified.

Why Other Options Are Wrong:
For a sales value of 300, 2.5% would be 7.50 rupees, which is less than the given commission. For 700, 2.5% would be 17.50 rupees, which is more than 12.50. For 900, 2.5% is 22.50 rupees, also incorrect. For 250, 2.5% is 6.25 rupees. None of these match the commission of Rs. 12.50. Only when the sales value is Rs. 500 do we obtain the correct commission amount.

Common Pitfalls:
A common error is to confuse 2.5% with 1/2 or to misplace the decimal when writing 2.5% as a fraction or decimal. Some learners attempt to divide 12.50 by 2.5 directly without converting the percentage properly, which gives 5 instead of the correct 500. Always remember that a percentage must be divided by 100 when converted into a decimal factor, so 2.5% equals 0.025, not 2.5. Using the correct factor ensures accurate results.

Final Answer:
The total value of cloth sold through the agent was Rs. 500.