Question

In the first four papers each of $100$ marks, Rishi got $95,72,73,83$ marks. 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 number he scored in fifth paper be $x$

Then average $i=\frac{95+72+73+83+x}{5}=\frac{323+x}{5}$

As per question

$75\le \frac{323+x}{5}$

Multiply by 5 both sides we get

$75\times 5\le \frac{323+x}{5}\times 5$

$375\le 323+x$

Add $-323$ both sides, we get

$375-323\le 323+x-323$

$\Rightarrow 52\le x$

As per question

$\frac{323+x}{5}<80$

Multiply by 5 both sides we get

$\frac{323+x}{5}\times 5<80\times 5$

$\Rightarrow 323+x<400$

Add $-323$ on both the sides we get

$323+x-323<400-323$

$\Rightarrow x=77$

Then, $52\le x<77$