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The average marks of students in a class in an exam is 80. If 5 students who scored an average of 40 marks in that exam are removed, then the average marks of the remaining students becomes 90. Find the number of students who appeared for the exam.
25
20
15
35
25
Use alligation or balance of total marks: the 5 students brought down the average by 40 marks each (80тИТ40=40), totaling a deficit of 5├Ч40=200 marks. This deficit was distributed among the remaining students, each gaining 90тИТ80=10 marks. Thus, remaining students = 200/10=20. Total students = 20+5=25.
Average marks of the class = 80, Number of excluded students = 5, Average marks of the excluded students = 40, Average marks of remaining students = 90
Total┬аMarks=Number┬аof┬аStudents├ЧAverage┬аMarks
Use alligation or balance of total marks: the 5 students brought down the average by 40 marks each (80тИТ40=40), totaling a deficit of 5├Ч40=200 marks. This deficit was distributed among the remaining students, each gaining 90тИТ80=10 marks. Thus, remaining students = 200/10=20. Total students = 20+5=25.
Forgetting to add the 5 excluded students back to the number of remaining students to find the total initial number of students.
Step 1: Assume total number of students
Let the total number of students who wrote the exam be x. The average marks of the class is 80.
Total┬аMarks┬аof┬аx┬аstudents=80x
Step 2: Calculate the marks of excluded students
It is given that 5 students have an average of 40 marks.
Sum┬аof┬аmarks┬аof┬а5┬аstudents=5├Ч40=200
Step 3: Set up the equation for remaining students
The number of remaining students is (xтИТ5) and their average marks become 90. Therefore, the total sum of marks of the remaining students is 90(xтИТ5).
80xтИТ200=90(xтИТ5)
Step 4: Solve for x
Expanding and rearranging the equation: 80xтИТ200=90xтИТ450тЯ╣90xтИТ80x=450тИТ200тЯ╣10x=250тЯ╣x=25.
x=25
A is correct because solving the linear equation 80xтИТ200=90(xтИТ5) yields x=25 total students.
Similar weighted average problems frequently appear in mixture and allegation questions in quantitative aptitude.
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