Question

if the median of x,x/2,x/8,x/5,x/6 and x/3 is 16 find x
a)64 b)30 c)60 d)15

Answer 1

Correct Answer= (c) 60

Given:-

$\small\sf{Median \: of } \: x, \frac{x}{2}, \frac{x}{8}, \frac{x}{5}, \frac{x}{6} \: and \: \frac{x}{3}$

Need To Find:-

The value of x

Solution:-

$\small\sf{Increasing \: Order} \: \frac{x}{8}, \frac{x}{6}, \frac{x}{5}, \frac{x}{3}, \frac{x}{2},x$

n=6

Median = 16

$\small\sf{Median} \: \frac{1}{2}[ \binom{6}{2}th \: + (\frac{6}{2} + 1)th \: ]$

$\frac{1}{2} [3 {}^{rd} + {4}^{th} ] = \frac{1}{2} [ \frac{x}{5} + \frac{x}{38} ]$

$16 = \frac{1}{2} \times \frac{8r}{15} ⇒x = 60$