Difficulty: Medium
Correct Answer: 192
Explanation:
Introduction / Context:
This question uses ratio relationships between three subject marks combined with an average condition. It is a straightforward algebra problem where we express all marks in terms of one variable and use the given average to solve.
Given Data / Assumptions:
- Average of marks in three subjects = 224.
- Let the marks in the three subjects be M1, M2 and M3.
- M1 = 2 * M2.
- M2 = 2 * M3.
- All marks are non negative numbers.
Concept / Approach:
First, we express all three marks in terms of the third subject. Then we use the average condition to determine their actual values. Finally, we extract the value of the second subject.
Step-by-Step Solution:
Step 1: Let M3 = x.Step 2: Then M2 = 2x (since the second is twice the third).Step 3: M1 = 2 * M2 = 2 * 2x = 4x.Step 4: Sum of marks = M1 + M2 + M3 = 4x + 2x + x = 7x.Step 5: Average of the three subjects = 224, so 7x / 3 = 224.Step 6: Multiply both sides by 3: 7x = 224 * 3 = 672.Step 7: Solve for x: x = 672 / 7 = 96.Step 8: M3 = 96, M2 = 2 * 96 = 192, M1 = 4 * 96 = 384.Step 9: The second subject marks are therefore 192.
Verification / Alternative check:
The sum of the marks is 384 + 192 + 96 = 672. The average is 672 / 3 = 224, which matches the given average, confirming that the derived values are consistent.
Why Other Options Are Wrong:
- 384 is the mark in the first subject, not the second.
- 96 is the mark in the third subject.
- 206 is not consistent with the required ratio relations and would not produce an average of 224 when used with matching values for the other two subjects.
Common Pitfalls:
- Mixing up the order of relationships, for example taking the third subject as twice the second rather than the reverse.
- Using the average directly as one of the subject marks without considering the ratio.
Final Answer:
The marks in the second subject are 192.
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