Quantity A is equal to 20% of B, and quantity B is equal to 25% of C.\nWhat percentage of C is quantity A?

Introduction / Context:
This problem checks understanding of chained percentage relationships between three quantities A, B, and C. It is very common in aptitude exams to link variables through percentages and then ask you to express one variable directly as a percentage of another. Mastering this type of question helps in many topics, including ratio, proportion, and basic algebra.

Given Data / Assumptions:

• A is 20% of B.
• B is 25% of C.
• We need to find A as a percentage of C.
• No absolute values are given, so we can comfortably work with symbolic or assumed values.

Concept / Approach:
Percentages can be converted into fractions or decimal multipliers. A being 20% of B means A = 0.20 * B. B being 25% of C means B = 0.25 * C. By substituting the second relation into the first, we can express A directly in terms of C. Once A is expressed as a decimal multiple of C, we can convert that multiple into a percent by multiplying by 100. This systematic substitution is the key idea behind the solution.

Step-by-Step Solution:
Step 1: Write A in terms of B: A = 20% of B = 20 / 100 * B = 0.20 * B.Step 2: Write B in terms of C: B = 25% of C = 25 / 100 * C = 0.25 * C.Step 3: Substitute the expression for B into the equation for A: A = 0.20 * (0.25 * C).Step 4: Multiply the decimals: 0.20 * 0.25 = 0.05.Step 5: So A = 0.05 * C, which means A is 5% of C.

Verification / Alternative check:
We can verify using assumed numerical values. Let C = 100 units. Then B = 25% of 100 = 25 units. Next, A = 20% of 25 = 5 units. If C is 100 units and A is 5 units, then A is 5 / 100 * 100% = 5% of C. This numerical check confirms the algebraic reasoning and gives the same answer.

Why Other Options Are Wrong:
10% would mean A = 0.10 * C, which is double the correct value and would require A to be 40% of B or B to be 50% of C, which is not given.
15% and 20% do not come from multiplying 20% and 25% correctly, and they ignore the fact that two successive reductions are involved.
8% is another distractor that cannot be derived from the given relationships.

Common Pitfalls:
A frequent error is to add or average the two percentages instead of multiplying them as factors. Another mistake is to mix up which quantity is a percentage of which, for example treating C as a percentage of B instead of the other way around. To avoid confusion, always write down the relationships clearly in equation form and use substitution carefully. Converting all percentages to decimals or simple fractions before multiplying also helps reduce calculation mistakes.

Final Answer:
Quantity A is 5% of quantity C.