Question : The average mark obtained by a class of 60 students is 65. The average marks of half of the students were found to be 85. The average marks of the remaining students are:
Option 1: 35
Option 2: 45
Option 3: 55
Option 4: 65
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Correct Answer: 45
Solution :
Let the average marks of the remaining 30 students be $p$.
So, $65=\frac{(30×85)+(30×p)}{60}$
⇒ $65 × 60 = 2550 + 30p$
⇒ $3900 = 2550 + 30p$
⇒ $30p = 3900 – 2550$
⇒ $p=\frac{1350}{30}$
$\therefore p=45$
Hence, the correct answer is 45.
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