The average score in Mathematics of a class increases by 10% if the total marks secured by a number of students who form 20% of the class strength and whose average score is 48 is not included in the calculation. What is the average score?
Question
The average score in Mathematics of a class increases by 10% if the total marks secured by a number of students who form 20% of the class strength and whose average score is 48 is not included in the calculation. What is the average score?
Solution
Let's break down the problem step by step:
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Let's assume the total strength of the class is 100 (for simplicity). So, 20 students have an average score of 48.
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The total marks secured by these 20 students is 20 * 48 = 960.
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Let's assume the average score of the entire class (including these 20 students) is 'x'. So, the total marks secured by the entire class is 100x.
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If we exclude the 20 students, the average score increases by 10%. So, the new average score is 1.1x.
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The total marks secured by the remaining 80 students is 80 * 1.1x = 88x.
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According to the problem, the total marks secured by the entire class (100x) is equal to the total marks secured by the 20 students (960) plus the total marks secured by the remaining 80 students (88x).
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So, we can set up the equation: 100x = 960 + 88x.
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Solving this equation gives: 12x = 960, so x = 80.
So, the average score of the entire class is 80.
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