Banking Quantitative Aptitude Sample Paper Quantitative Aptitude Sample Paper-10

There are three positive numbers, one-third of average of all the three numbers is 8 less than the value of the highest number. Average of the lowest and the second lowest number is 8. Which is the highest number?

A) 11

B) 14

C) 10

D) 9

E) 13

Correct Answer: A

Solution :

Let the three positive numbers are x, y and z in increasing order, and average of three numbers be A.

According to the question,

\[\Rightarrow \] \[\frac{x+y+z}{3}=A\] (i)

Given, \[z-\frac{A}{3}=8\]

\[z-\frac{x+y+z}{9}=8\] ... (ii)

Also given that, \[\frac{x+y}{2}=8\]

\[x+y=16\] ... (iii)

Put the value of \[(x+y)\] in Eq. (ii), we get

\[z-\frac{16+z}{9}=8\]

\[\Rightarrow \] \[\frac{9z-16-z}{9}=8\]

\[\Rightarrow \] \[8z=72+16=88\]

\[\Rightarrow \] \[z=\frac{88}{8}=11\]

So, highest number is 11.