Difficulty: Easy
Correct Answer: 69
Explanation:
Introduction:
This is a straightforward average marks question where the overall average and the averages of certain groups of subjects are given. You are asked to find the marks in the remaining subject.
Given Data / Assumptions:
Average marks in five subjects = 82. Average marks in the first two subjects = 86.5. Average marks in the last two subjects = 84. Marks in the third subject = unknown (let this be x).
Concept / Approach:
The principle is to convert averages into totals, then use subtraction to isolate the unknown subject. If S1 and S2 are first two subjects, S3 is the third, and S4 and S5 are the last two, then: Total in all five = 5 * 82. Total in first two = 2 * 86.5. Total in last two = 2 * 84. Then S3 = Total in all five - Total in first two - Total in last two.
Step-by-Step Solution:
Step 1: Total marks in all five subjects = 5 * 82. Total in all five = 410. Step 2: Total marks in the first two subjects = 2 * 86.5 = 173. Step 3: Total marks in the last two subjects = 2 * 84 = 168. Step 4: Compute marks in the third subject. Marks in third subject = 410 - 173 - 168. Marks in third subject = 410 - 341 = 69.
Verification / Alternative Check:
Take example marks: let first two be 86.5 and 86.5 (sum 173), third be 69, and last two be 84 and 84 (sum 168). Then total = 173 + 69 + 168 = 410. Average = 410 / 5 = 82, which matches the given overall average.
Why Other Options Are Wrong:
67, 71, 73, 75: None of these values satisfy the equation obtained from the total sum 410. Substituting them would result in an overall average different from 82.
Common Pitfalls:
Students sometimes confuse the direction of subtraction and may incorrectly add averages instead of totals. Another common mistake is to divide the remaining total by the wrong number of subjects. Here, the third subject is a single subject, so do not divide again after subtraction.
Final Answer:
The marks obtained in the third subject are 69.
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