The mean and median of the data x,y,z are 50 and 35 respectively, where x

The mean and median of the data $x, y, z$ are 50 and 35 respectively, where $x < y < z .$ If $z - x = 55$ they $y - x =$

A
8
B
7
C
3
D
5

Solution:

We have

Mean = 50 and, Median = 35

$\Rightarrow \frac{x + y + z}{3} = 50$ and $y = 35$

$\Rightarrow x + y + z = 150$ and $y = 35 \Rightarrow x + z = 115$

But, $z - x = 55$ (given). Therefore, $x = 30$

Hence, $y - x = 35 - 30 = 5$

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