### If average of 20 observations$\mathbf{x}_{1}, \mathbf{x}_{\mathbf{2}}, \ldots \ldots \mathbf{x}_{\mathbf{2 0}}$ is y, then the average of x1 – 101, x2 – 101, x3 – 101, . . . . . x20 – 101 is :is :

A. y – 20 B. y – 101 C. 20y D. 101y Answer: Option B
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### Solution(By Apex Team)

$\begin{array}{l}\Rightarrow\Large\frac{x_1+x_2+x_3+x_4+\ldots+x_{20}}{20}=y\\ \Rightarrow x_1+x_2+x_3+x_4+\ldots+x_{20}=20y\\ =\Large\frac{x_1-101+x_2-101+x_3-101+x_4-101+\ldots.+x_{20}-101}{20}\\ =\Large\frac{\left(x_1+x_2+x_3+x_4+\ldots+x_{20}\right)-20\times101}{20}\\ =\Large\frac{20y-20\times101}{20}\\ =y-101\end{array}$

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### If the arithmetic mean of 0, 5, 4, 3 is a, that of -1, 0, 1, 5, 4, 3 is b and that of 5, 4, 3 is c, then the relation between a, b, and c is.

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