Multiple choice

The students of a class are divided into 3 groups depending on their performance in a test – the top, middle and bottom. The top group consists of 45% of the students, the middle group consists of 30% of the students and the rest are in the bottom group. The average marks of the bottom group are 20, those of the middle are 25 while the average marks for the entire class are 26. Find the average marks of the top group.

  1. 7

  2. 12

  3. 22

  4. 30
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let total students be 100. Top=45, Middle=30, Bottom=25. Total marks = 100 * 26 = 2600. Bottom marks = 25 * 20 = 500. Middle marks = 30 * 25 = 750. Top marks = 2600 - 500 - 750 = 1350. Average of top = 1350 / 45 = 30.

AI explanation

Using the method of alligation, the overall average is 26 and the middle group average is 25, so the difference between the overall average and the middle average is 1. This means the bottom group (average 20) pulls the average down by 6 points from the middle, which corresponds to the 25% of students in the bottom group. Therefore, the top group must pull the average up proportionally for its 45% of students; solving the weighted average equation 0.45 * (top average) + 0.30 * 25 + 0.25 * 20 = 26 gives 0.45 * (top average) = 13.5. Dividing 13.5 by 0.45 yields an average of 30 for the top group.

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