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
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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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