### There are three positive numbers. One third of the average of all the three numbers is 8 less than the value of the highest number. The average of the lowest and the second lowest number is 8. What is the highest number?

**A.** 11

**B.** 14

**C.** 10

**D.** 9

## Show Answer

###
Answer-A

Solution-

__Solution(By Apex Team)__

Let the three positive numbers in increasing order be a, b and c and the average of these numbers be be A.
Then,
$\begin{array}{l}\left(\Large\frac{a+b+c}{3}\right)=A\ldots.(i)\\
\text{ Given, }\\
c-\frac{A}{3}=8\\
\Rightarrow c-\left(\Large\frac{a+b+c}{9}\right)=8\ldots..(ii)\\
\text{Also given,}\\
\left(\Large\frac{b+a}{2}\right)=8\\
\Rightarrow a+b=16…..\left(iii\right)\end{array}$
Putting the value of (a + b) in equation (ii), we get
$\begin{array}{l}\Rightarrow c-\left(\Large\frac{16+c}{9}\right)=8\\
\Rightarrow9c-16-c=72\\
\Rightarrow8c=72+16\\
\Rightarrow8c=88\\
\Rightarrow c=11\\
\therefore\text{ Highest number }=11\end{array}$