The present age of Riya is four times the present age of Siya, and the age of Riya is 24 years. What is the difference between the ages of Riya and Siya?

Introduction / Context:
This is a simple age ratio problem involving two people, Riya and Siya. Riya's age is given to be a multiple of Siya's age, and Riya's actual age is specified. We must find the difference between their ages. This type of problem tests basic proportional reasoning and subtraction.

Given Data / Assumptions:
The present age of Riya is four times the present age of Siya. Riya is 24 years old at present. We need to find the age difference between Riya and Siya. Ages are in years and assumed to be whole numbers.

Concept / Approach:
When one person's age is a multiple of another's, we can express the smaller age as a variable and the larger as a multiple of that variable. Here, Riya's age equals 4 times Siya's age. Knowing Riya's age allows us to divide by 4 to find Siya's age. The difference between their ages is then easily obtained by subtraction.

Step-by-Step Solution:
Step 1: Let Siya's present age be S years.Step 2: Riya's present age is four times Siya's age, so Riya's age is 4S years.Step 3: It is given that Riya is 24 years old, so 4S = 24.Step 4: Solve for S: S = 24 / 4 = 6 years.Step 5: The difference between their ages is Riya's age minus Siya's age, which is 24 - 6 = 18 years.

Verification / Alternative check:
Check that Riya's age is indeed four times Siya's: 4 * 6 = 24, which matches Riya's given age. The computed difference of 18 years is therefore consistent with the problem data. There are no additional conditions to check, so the solution is straightforward and complete.

Why Other Options Are Wrong:
A difference of 2, 12, or 6 years would imply Siya's age is 22, 12, or 18 respectively if Riya is 24. None of these ages satisfies the condition that Riya is four times Siya's age. Only when Siya is 6 years old does the four times condition hold, giving a difference of 18 years.

Common Pitfalls:
A common mistake is to interpret "four times the age" incorrectly and either subtract 4 or add 4 instead of multiplying by 4. Another error is to misplace which person is older. Carefully translating the phrase "four times the age" into a multiplication equation prevents such confusion.

Final Answer:
The difference between the ages of Riya and Siya is 18 years.