The Average Marks Scored by Two Groups X and Y of Students Are 70 and 75 Respectively. Four Students Are Moved from Group Y to Group X, Thereby Interchanging the Average Marks of the Two Groups. - Mathematics

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MCQ

Solve the following question and mark the best possible option.
The average marks scored by two groups X and Y of students are 70 and 75 respectively. Four students are moved from group Y to group X, thereby interchanging the average marks of the two groups. Find the total number of students in two groups put together, if the average marks scored by the four students who moved are 85.

Options

  • 12

  • 20

  • 27

  • 30

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Solution

Let the number of students in section A be x and section B be y.
Total marks scored by the students will be 70x and 75y.
75y – 4 x 85 = 70(y – 4)75y – 340 = 70y – 280
⇒ 5y = 60
⇒ y = 12
Similarly 70x + 340 = 75(x + 4)
⇒ 5x = 40
⇒ x = 8
Thus the total number of students = 12 + 8 = 20

Concept: Average and Age
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