Multiple choice

During his weekly tests, Mohan's average was 85 in 7 subjects. Out of these, the difference between the highest marks and the second highest marks is equal to the difference between the second highest marks and the third highest marks, and it is equal to 5. If we eliminate these three subjects, the average marks become 76. What is the highest score of Mohan?

  1. 89

  2. 90

  3. 92

  4. 102
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D Correct answer
Explanation

Let the marks be x, x-5, x-10. Sum of 7 subjects = 7 * 85 = 595. Sum of remaining 4 subjects = 4 * 76 = 304. Sum of top 3 = 595 - 304 = 291. x + x-5 + x-10 = 291 => 3x = 306 => x = 102.

AI explanation

Using the basic average formula, the total marks for 7 subjects is 85 times 7, which equals 595. Eliminating the top three subjects leaves 4 subjects with an average of 76, making their sum 76 times 4, or 304. The sum of the top three marks is 595 minus 304, giving 291. Let the third highest marks be x, making the second highest x + 5 and the highest x + 10. Setting the sum of these three equal to 291 gives the equation 3x + 15 equals 291. Solving this yields x equals 92, so the highest score is 92 + 10, which is 102.

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