After selling 5% of a certain quantity of sugar, 95 kg of sugar still remains.\nWhat was the original quantity of sugar before any part of it was sold?

Introduction / Context:
This question tests basic percentage application in the context of remaining quantity after a small portion is sold. It is a classic reverse percentage problem where we know what remains and the percentage that this remaining quantity represents of the original stock. Such problems are common in aptitude tests dealing with stock, inventory, and simple commercial arithmetic.

Given Data / Assumptions:

• A shopkeeper sells 5% of a stock of sugar.
• After this sale, 95 kg of sugar remain.
• We assume there is no wastage or additional sugar added.
• We are asked to find the original total quantity of sugar.

Concept / Approach:
If 5% of the sugar is sold, that means 95% of the original quantity is left. The key idea is to interpret the remaining quantity as a percentage of the original. Once we know that 95 kg represents 95% of the stock, we can set up a simple proportion to find 100% of the stock. This is a straightforward reverse percentage calculation where remaining quantity = percentage factor * original quantity.

Step-by-Step Solution:
Step 1: Let the original quantity of sugar be Q kg.Step 2: Since 5% is sold, the remaining fraction is 100% - 5% = 95% of Q.Step 3: In decimal form, 95% = 95 / 100 = 0.95.Step 4: We are told that 0.95 * Q = 95 kg.Step 5: Solve for Q: Q = 95 / 0.95 = 100 kg.

Verification / Alternative check:
Check by forward calculation. If the original quantity is 100 kg, then 5% of 100 kg is 5 kg sold. The remaining sugar is 100 kg - 5 kg = 95 kg. This matches the quantity given in the problem, so the original quantity of 100 kg is confirmed to be correct.

Why Other Options Are Wrong:
19 kg would make 95% equal to 19 kg, which is not true, because 5% of 19 kg is 0.95 kg and the remaining amount would be much smaller than 95 kg.
55 kg as 95% would give original 55 / 0.95 = 57.89 kg, but this does not match the structure of the problem and is not among logically expected values.
95 kg would incorrectly assume that there was no sale at all, which contradicts the information about a 5% sale.
75 kg as original amount would leave 0.95 * 75 = 71.25 kg, which is not equal to the specified 95 kg.

Common Pitfalls:
Many students mistakenly treat the remaining 95 kg as 5% of the original rather than 95%. Others subtract percentages instead of using a simple multiplication and division approach. It is helpful to always convert percentages into decimal factors and to remember that remaining quantity equals percentage remaining times original quantity. Writing the relationship as an equation makes the reasoning clear and avoids mental shortcuts that can lead to errors.

Final Answer:
The original quantity of sugar was 100 kg.