If 2% of a quantity a is equal to b, then b% of 10 is numerically equal to which of the following expressions in terms of a?

Introduction / Context:
This question again tests the ability to convert symbolic percentage relations into algebra and to simplify them into an expression in terms of a single variable. We are told how b relates to a, and then asked to compute b% of a numerical quantity, expressing the result purely in terms of a. Such symbolic percentage problems help in building strong foundations for handling more complex algebraic percentage scenarios in exams and real life applications.

Given Data / Assumptions:

• Two percent of a is equal to b, that is 2% of a = b.
• We need to find b% of 10.
• The final expression must be written using a only.
• All percentage operations follow usual arithmetic rules.

Concept / Approach:
The main approach is to write the given percentage relation as a formula. From 2% of a = b, we find b in terms of a. Then we interpret b% of 10 as (b / 100) multiplied by 10. Substituting for b leads to a numerical coefficient times a. Finally, we express this coefficient in the form shown in the answer choices, which use phrases like “20% of a/100” to represent the fraction of a.

Step-by-Step Solution:
Step 1: Express 2% of a. We have 2% of a = (2 / 100) * a = 0.02 * a. Step 2: Given that 2% of a equals b, we get b = 0.02 * a. Step 3: Now compute b% of 10. By definition, b% of 10 = (b / 100) * 10. Step 4: Substitute b = 0.02 * a into the expression: b% of 10 = (0.02 * a / 100) * 10. Step 5: Combine constants. First compute 0.02 * 10 = 0.2. Step 6: So b% of 10 = 0.2 * a / 100. Step 7: This is the same as 20% of a divided by 100, because 20% of a is (20 / 100) * a = 0.2 * a. Step 8: Therefore b% of 10 equals 20% of a / 100.

Verification / Alternative check:
To check numerically, choose a convenient value such as a = 1000. Then 2% of 1000 is 20, so b = 20. Now b% of 10 means 20% of 10, which equals 2. Next evaluate 20% of a / 100 for a = 1000. First find 20% of a: 20% of 1000 is 200. Then divide by 100 to get 200 / 100 = 2. The numeric result matches exactly, confirming that the expression 20% of a / 100 is equivalent to b% of 10.

Why Other Options Are Wrong:
Option a, 200% of a, equals 2 * a, which is far larger than the tiny fraction we obtained. Option c, 20% of a / 10, simplifies to 0.2 * a / 10 = 0.02 * a, which is ten times too large. Option d, 200% of a / 10, equals 2 * a / 10 = 0.2 * a, which is also much larger than the correct expression. Therefore only “20% of a/100” correctly represents the value of b% of 10 in terms of a.

Common Pitfalls:
It is easy to confuse percent and decimal forms or to forget to divide by 100 when converting percentages. Another typical error is to misread 2% of a = b as b% of a = 2, completely changing the relationship. To stay accurate, always write percentage expressions as fractions or decimals explicitly and perform substitutions step by step, checking the units and magnitudes at each stage.

Final Answer:
The value of b% of 10 is equal to 20% of a/100.