There are 50 students in a class and the average mark scored by the class in Maths is 65 out of 100. The total marks scored by all the students except Karan and Arjun is 3080. If the marks scored by Karan & Arjun are same, what are the marks scored by Arjun?

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Solution

The correct option is C
85

$A v e r a g e$ $=$ $\frac{T o t a l m a r k s}{T o t a l n u m b e r o f s t u d e n t}$

$65$ $=$ $\frac{3080 + M a r k s s c o r e d b y A r j u n + M a r k s s c o r e d b y K a r a n}{50}$

Since marks scored by Arjun = Marks scored by Karan

Marks scored by Arjun + Marks scored by Karan = 2 $\times$ Marks scored by Arjun.

So, 65 $\times$ 50 = 3080 + 2 $\times$ Marks scored by Arjun

So, marks scored by Arjun
$= \frac{3250 - 3080}{2}$
$= \frac{170}{2}$
= 85 marks.

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