Quantitative Aptitude Ques 5
Question: 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?
Options:
A) 11
B) 14
C) 10
D) 9
E) 13
Show Answer
Answer:
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.
BETA
