Question

The ages of three friends are a, b and c years such that a < c < b. If median age is 24 years, and ratio of their ages is 4 : 5 : 3, then the average of their ages is

• A. 12 years
• B. 20 years
• C. 32 years
• D. 28 years

Answer 1

The correct option is C 32 years

When number of terms (n) is odd, then median is $(\frac{n+1}{2}{)}^{th}$
Here, n = 3.

$\Rightarrow Median=(\frac{3+1}{2}{)}^{th}=2^{nd}$
Observation = c

$\Rightarrow c=24$ ($\therefore$Median = 24)
Also, given that the ratio of the ages is 4 : 5 : 3.

Consider, the ratio factor to be x.
$\Rightarrow 3x=24$ ($\therefore$ c = 3x)
$\Rightarrow x=8$

∴ Mean age of three friends $=\frac{4x+5x+3x}{3}$
$=4x$
$=4\times 8$
= 32 years

Hence, the correct answer is option c.