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In the university examination last year, Rajesh scored 65% in English and 82% in History. What is the minimum percent he should score in Sociology, which is out of 50 marks (if English and History were for 100 marks each), if he aims at getting 78% overall?
  • a)
    94%
  • b)
    92%
  • c)
    98%
  • d)
    96%
  • e)
    None of these
Correct answer is option 'D'. Can you explain this answer?
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To find the minimum percent Rajesh should score in Sociology, we can use the weighted average formula.

Weighted Average = (Percentage in Subject 1 * Weightage of Subject 1 + Percentage in Subject 2 * Weightage of Subject 2 + Percentage in Subject 3 * Weightage of Subject 3) / Total Weightage

From the question, we know that English and History were for 100 marks each, while Sociology is out of 50 marks. Therefore, the weightage of English and History is 1, and the weightage of Sociology is 0.5.

We also know that Rajesh aims to get an overall percentage of 78%. Let's assume the percentage he needs to score in Sociology is x.

Now, we can set up the equation:

(65 * 1 + 82 * 1 + x * 0.5) / (1 + 1 + 0.5) = 78

Simplifying the equation:

(65 + 82 + 0.5x) / 2.5 = 78

147 + 0.5x = 195

0.5x = 48

x = 96

Therefore, the minimum percent Rajesh should score in Sociology to achieve an overall percentage of 78% is 96%.

Hence, the correct answer is option D) 96%.
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