Question

The average of $8$ numbers is $20$. The average of first two numbers is $15\frac{1}{2}$ and that of next three is $21\frac{1}{3}$. If the sixth number be less than the seventh and eighth numbers by $4$ and $7$, respectively, then find the eighth number?

• A. $20$
• B. $22$
• C. $25$
• D. $27$

Answer 1

The correct option is C $25$

Let the eighth number be $x$

Then sixth number $=x-7$.

Seventh number $=(x-7)+4-(x-3)$

So, $(2\times 15\frac{1}{2})+(3\times 21\frac{1}{3})+(x-7)+(x-3)+x=8\times 20$

$\Rightarrow 31+64+3x-10=160$

$\Rightarrow 3x=75$

$\Rightarrow x=25$