Question

If the mean of ten consecutive odd numbers is $120$, then the mean of the first five odd numbers among them is

• A. $113$
• B. $115$
• C. $114$
• D. $116$

Answer 1

The correct option is B $115$

Let, ten consecutive odd number be

$2x+1,2x+3,......,2x+19$

Hence, $(2x+1)+(2x+3)+.....+(2x+19)$ $=10\times 120$ ...... (sum of observations$=$Mean $\times$ No. of observation)

$\Rightarrow 20x+100=1200$

$\Rightarrow x=\frac{1100}{20}=55$

Mean of first five odd numbers

$=\frac{(2x+1)+(2x+3)+....+(2x+9)}{5}$

$=\frac{(x\times 10)+(1+3+5+7+9)}{5}$

$=\frac{(10\times 55)+25}{5}=\frac{575}{5}=115$

Option $\left(2\right)$.