The average of the marks obtained in three subjects is 224. The marks in the first subject are twice the marks in the second subject and the marks in the second subject are twice the marks in the third subject. What are the marks in the second subject?

Introduction:
This problem involves an average of three subject marks and given relationships between those marks. It tests understanding of how to translate statements about relative sizes into algebraic equations and then use the average information to find individual values. Such questions are typical in aptitude tests on ratios, averages and basic algebra.

Given Data / Assumptions:
- There are three subjects with marks in each subject. - The average of the three subject marks is 224. - Marks in the first subject are twice the marks in the second subject. - Marks in the second subject are twice the marks in the third subject. - We must find the marks obtained in the second subject.

Concept / Approach:
If we let the third subject mark be a basic variable, then the other two marks can be written in terms of this variable using the given relationships. The average of three numbers is equal to their total sum divided by 3. Using the given average, we can find the total sum, then set up an equation in terms of the variable and solve for it. Finally, we compute the middle subject mark using the relationship.

Step-by-Step Solution:
Step 1: Let the marks in the third subject be x. Step 2: The second subject marks are twice the third subject, so second subject marks = 2x. Step 3: The first subject marks are twice the second subject, so first subject marks = 2 * 2x = 4x. Step 4: The three subject marks are therefore 4x, 2x and x. Step 5: Given that the average of these three marks is 224, total marks = 3 * 224 = 672. Step 6: Sum of the three marks in terms of x is 4x + 2x + x = 7x. Step 7: Set up the equation 7x = 672. Step 8: Solve for x: x = 672 / 7 = 96. Step 9: Second subject marks = 2x = 2 * 96 = 192.

Verification / Alternative Check:
If the third subject marks are 96, the second subject marks are 192 and the first subject marks are 384. Sum of marks = 96 + 192 + 384 = 672. The average is 672 / 3 = 224, which matches the given average. The relationship conditions are also satisfied: first subject 384 is twice second subject 192, and second subject 192 is twice third subject 96. This confirms that the calculation is correct.

Why Other Options Are Wrong:
Option 96 is the third subject mark, not the second subject mark. Option 128 and option 224 do not satisfy both relationships at the same time when used as the second subject mark. Option 256 leads to a total that does not give an average of 224 while maintaining the required ratios.

Common Pitfalls:
A common mistake is to confuse which subject is twice which and assign the ratios incorrectly. Another error is to forget to multiply the average by 3 to get the total sum. Keeping a clear representation such as 4x, 2x and x helps avoid these issues and makes the algebra straightforward.

Final Answer:
The marks obtained in the second subject are 192.