Question

Average of $8$ numbers is $20$, that of the first two is $15.5$ and that of the next three is $21\frac{1}{3}$, the $6^{th}$ is less than the $7^{th}$ by $4$ and $7$ less than the $8^{th}$. The last number is:

• A. $25$
• B. $28$
• C. $35$
• D. $32$

Answer 1

Answer: (A)

$25$

Sum of $8$ numbers $=20\times 8=160$
Sum of first $5$ numbers $=15.5\times 2+\frac{64}{3}\times 3$
$=31+64$
$=95$
Sum of last $3$ numbers $=(160=95)=65$
Let $6^{th},7^{th}$ and $8^{th}$ number be $x,y,z$ respectively
$y-x=4.....\left(1\right)$
$z-x=7.....\left(2\right)$
$z-y=3.....\left(3\right)$
$x+y+z=65.....\left(4\right)$ [From $\left(1\right)$$and$(2)$]From$(3)$and$(4)z - x = 7\Rightarrow z = 25$.