JEE MAIN - Mathematics (2019 - 9th April Evening Slot - No. 8)
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 $${y \over x}$$ is equal to
$${7 \over 2}$$
$${8 \over 3}$$
$${9 \over 4}$$
$${7 \over 3}$$
Explanation
Given ten numbers are 10, 22, 26, 29, 34, x,
42, 67, 70, y.
As the numbers are in increasing order so
Mediun = $${{34 + x} \over 2}$$ = 35
$$ \Rightarrow $$ x = 36
Also given mean = 42
$$ \Rightarrow $$ $${{10 + 22 + 26 + 29 + 34 + x + 42 + 67 + 70 + y} \over {10}}$$ = 42
$$ \Rightarrow $$ $${{300 + x + y} \over {10}}$$ = 42
$$ \Rightarrow $$ 300 + x + y = 420
$$ \Rightarrow $$ 336 + y = 420
$$ \Rightarrow $$ y = 84
$$ \therefore $$ $${y \over x} = {{84} \over {36}}$$ = $${7 \over 3}$$
As the numbers are in increasing order so
Mediun = $${{34 + x} \over 2}$$ = 35
$$ \Rightarrow $$ x = 36
Also given mean = 42
$$ \Rightarrow $$ $${{10 + 22 + 26 + 29 + 34 + x + 42 + 67 + 70 + y} \over {10}}$$ = 42
$$ \Rightarrow $$ $${{300 + x + y} \over {10}}$$ = 42
$$ \Rightarrow $$ 300 + x + y = 420
$$ \Rightarrow $$ 336 + y = 420
$$ \Rightarrow $$ y = 84
$$ \therefore $$ $${y \over x} = {{84} \over {36}}$$ = $${7 \over 3}$$
Comments (0)
