A dishonest dealer claims to sell goods at cost price but actually uses a weight of only 875 grams instead of a true kilogram (1000 grams). What is his gain in percentage?

Introduction / Context:
This cheating problem is similar to the previous one but with a different false weight. The dealer pretends to sell 1 kilogram but actually delivers only 875 grams, while charging the price of 1 kilogram at the supposed cost price. It tests the ability to compute effective profit percentage when the quantity delivered is less than the quantity charged and to express the final answer as a mixed fraction percent.

Given Data / Assumptions:

• Dealer claims to sell 1 kilogram at cost price.
• Actual quantity delivered is 875 grams.
• Customer pays for 1000 grams at cost price.
• Let the cost price of 1 kilogram be C rupees.
• We need the gain percentage.

Concept / Approach:
As before, the dealer really spends only the cost of 875 grams, but charges the customer for 1000 grams. So selling price is C rupees, and cost price of the goods actually delivered is proportional to 875 grams. The profit is the difference between these two amounts. Profit percentage is calculated on the cost of 875 grams, not on the cost of 1 kilogram. The fraction obtained must then be converted into a percentage and simplified into a mixed fraction form like 14 2/7%.

Step-by-Step Solution:
Step 1: Let cost price of 1000 grams be C rupees.Step 2: Cost per gram = C / 1000.Step 3: Cost of 875 grams = 875 * (C / 1000) = 0.875C.Step 4: Selling price SP for claimed 1 kilogram = C rupees.Step 5: Profit = SP - CP = C - 0.875C = 0.125C.Step 6: Profit percentage = (0.125C / 0.875C) * 100.Step 7: Ratio 0.125 / 0.875 = 125 / 875 = 1 / 7.Step 8: Therefore profit percentage = (1 / 7) * 100 = 100 / 7%.Step 9: 100 / 7 = 14 2/7% when expressed as a mixed fraction.

Verification / Alternative check:
Use a numerical example with C = Rs 100 for 1000 grams. Cost of 875 grams = 87.5 rupees. The dealer charges Rs 100. Profit = 100 - 87.5 = 12.5 rupees. Profit percentage = 12.5 / 87.5 * 100 = (1 / 7) * 100 = 14 2/7%. This matches the algebraic result quite precisely and confirms the correctness of our computations and the fraction simplification.

Why Other Options Are Wrong:
Option A (17%) is larger than the correct value and would correspond to a much smaller true quantity being given. Option B (14 5/7%) is close but still slightly larger than the true percentage and corresponds to a different false weight. Option D (14%) is a rounded value and does not exactly match the fraction 1/7. Only option C, 14 2/7%, correctly represents 100 / 7% and matches our detailed calculations.

Common Pitfalls:
Some candidates take profit percentage over 1000 grams instead of 875 grams, leading to 12.5% instead of 14 2/7%. Others incorrectly reduce the fraction or round too early, which causes them to miss the precise mixed fraction form. Always compute profit percentage on the cost of actual goods given and only simplify fractions at the end to avoid rounding errors.

Final Answer:
The dishonest dealer gains 14 2/7% by using an 875 gram weight instead of a true kilogram.