Question

In the first four papers of $100$ marks each, Rishi got $95,72,73,83$ marks respectively. If he wants an average of greater than or equal to $75$ marks and less than $80$ marks, find the range of marks he should score in the fifth paper.

• A. $52\le x<77$
• B. $25<x<75$
• C. $75<x<80$
• D. $73<x<100$

Answer 1

The correct option is A $52\le x<77$

Let the marks to be scored in the 5th paper be x
$average=\frac{95+72+73+83+x}{5}$
$=\frac{323+x}{5}$ ...(i)
It is given that the average should be atleast 75 marks and less than 80marks
Therefore applying the above condition
$75\le \frac{323+x}{5}<80$
$75\left(5\right)\le 323+x<80\left(5\right)$
$375\le (323+x)<400$
$52\le x<77$
Hence answer is A