Question

The mean and the median of the following ten numbers in increasing order
$10,22,26,29,34,x,42,67,70,y$
are $42$ and $35$ respectively, then $\frac{y}{x}$ is equal to :

• A. $\frac{7}{2}$
• B. $\frac{8}{3}$
• C. $\frac{7}{3}$
• D. $\frac{9}{4}$

Answer 1

The correct option is C $\frac{7}{3}$

Mean $=42$
$\Rightarrow \frac{10+22+26+29+34+x+42+67+70+y}{10}=42$
$\Rightarrow x+y=120$
Since there are $10$ terms, median will be mean of middle two terms.
Median $=\frac{34+x}{2}=35\Rightarrow x=36$
$\therefore y=84$
Hence, $\frac{y}{x}=\frac{7}{3}$