Question

The average of $15$ numbers is $18$. The average of first $8$ is $19$ and that last $8$ is $17$, then the $8th$ number is

• A. $15$
• B. $16$
• C. $18$
• D. $20$

Answer 1

The correct option is C $18$

Average $=\frac{Sumofnumbers}{No.ofnumbers}$
$18=\frac{Sumofnumbers}{15}$
Sum of numbers $=18\times 15=270$
Average of first $8$ numbers
$=\frac{Sumoffirst8numbers}{8}$
sum of first $8$ nos. $=19\times 8=152$
Average of last $8$ nos. $=\frac{Sumoflast8nos.}{8}$
Sum of last $8$ nos. $=17\times 8=136$
Eight number $=$ Sum of first $8$ nos. $+$ sum of last $8$ nos. - sum of $15$ nos.
$=152+136-270=288-270$
$=18$