Question : The average mark obtained in a test by the three students is $x$. If the marks of a new student are also considered, then the average mark increases by 2. What are the marks secured by the new student in the test?
Option 1: $x$ + 4
Option 2: $x$ + 6
Option 3: $x$ + 8
Option 4: $x$ + 2
Correct Answer: $x$ + 8
Solution :
Let's see the average mark obtained by the three students as $x$
The total marks obtained by the three students is 3$x$
New average = $x$ + 2
⇒ The total marks obtained by all students = 4($x$ + 2)
Let the marks obtained by the new student be $y$
So, 3$x$ + $y$ = 4($x$ + 2)
⇒ 3$x$ + $y$ = 4$x$ + 8
⇒ $y$ = 4$x$ + 8 − 3$x$
⇒ $y$ = $x$ + 8
Hence, the correct answer is $x$ + 8.
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