Question

In a test, the average marks scored by four students is 80. If the marks scored by the 5th student is also counted, the average rises to 81. What would the marks scored by the 5th student be?

• A. 81 marks
• B. 84 marks
• C. 85 marks
• D. 90 marks

Answer 1

The correct option is C 85 marks

$Average=\frac{Totalmarks}{Totalnumberofstudents}$

Let the total marks scored by the first four students be T.

$⟹Average=80=\frac{T}{4}$
$⟹T=320$

Now, counting the marks scored by the 5th student, we get the total marks as:

$Marksscoredbythe5thstudent=K$

$Totalmarks=T+K=320+K$

$Average=\frac{320+K}{5}=81$

Solving this, we get:

$\left(\frac{320+K}{5}\right)\times 5=81\times 5$

$⟹320+K=405$

$⟹(320+K)–320=405–320$

$⟹K=405–320$

$⟹K=85$

Hence, the 5th student would have scored 85 marks.