The average marks obtained in a test by three students is x. If the marks of a new student is also considered, then the average marks increases by 2. What is the marks secured by the new student in the test?

The average marks obtained in a test by three students is x.

total marks obtained in a test by three students = 3x    Eq.(i)

If the marks of a new student is also considered, then the average marks increases by 2.

average marks obtained in a test by four students = x+2

total marks obtained in a test by four students = 4(x+2)    Eq.(ii)

Marks secured by the new student in the test = Eq.(ii)-Eq.(i)

= 4(x+2)-3x

= 4x+8-3x

= x+8