### The average of odd numbers up to 100 is

A. 49 B. 50.5 C. 50 D. 100 Answer: Option C

### Solution(By Apex Team)

Sum of odd numbers upto 100 = 1 + 3 + 5 +…..+ 99 $\begin{array}{l}=\large\frac{50}{2}\left[2+\left(50-1\right)\times2\right]\\ =2500\end{array}$ [∵ Sum of n terms of an A.P. with first term a and common difference] $\begin{array}{l}\left[d=\frac{n}{2}\left\{2n+\left(n-1\right)\times d\right\}\right]\\ \text{∴ Required average}\\ =\Large\frac{2500}{50}\\ =50\end{array}$

A. 20
B. 21
C. 28
D. 32

A. 18
B. 20
C. 24
D. 30

A. 10 years
B. 10.5 years
C. 11 years
D. 12 years