Question

Let $x$ denote the mean of the observations $1,3,5,a,9$ and $y$ denote the mean of the observations $2,4,b,6,8$ where $a,b>0$ .If $x=y$ ,the value of $2(a-b)$ is ?

• A. $2$
• B. $38$
• C. $8$
• D. $-4$
• E. $4$

Answer 1

Answer: (E)

$4$

Answer 2

Given that:

Let $x$ denote the mean of the observations $1,3,5,a,9$ and $y$ denote the mean of the observations $2,4,b,6,8$ where $a,b>0$

If $x=y$ ,the value of $2(a-b)$ would be determine as follows

i.e. For observation $1,3,5,a,9$

mean$(x)=\dfrac{1+3+5+a+9}{5}$

$x=\dfrac{18+a}{5}$

Similarly for observation $2,4,b,6,8$

mean$(y)=\dfrac{2+4+b+6+8}{5}$

$(y)=\dfrac{20+b}{5}$

Now according to the question, $x=y$

$⇒\dfrac{18+a}{5}=\dfrac{20+b}{5}$

$⇒18+a=20+b$

$⇒a-b=2$

$⇒2(a-b)=2×2$

$⇒2(a-b)=4$ (_Ans.)