Question

The average of $80$ numbers is $42.$ When $5$ more numbers are included, then the average of $85$ numbers becomes $45.$ The average of $5$ numbers is

• A. $82$
• B. $89$
• C. $93$
• D. $98$

Answer 1

The correct option is C $93$

Average of $80$ numbers $=42$
$\therefore$ Sum of $80$ numbers $=80\times 42$
Average of $85$ numbers $=45$
$\therefore$ Sum of $85$ numbers $=85\times 45$
Hence, sum of $5$ numbers $=85\times 45-80\times 42$
Average of five numbers $=\frac{85\times 45-80\times 42}{5}$
$=85\times 9-16\times 42$
$=93$