Q258 / 270 · NDA 2022 (Phase 1) · Mathematics

The algebraic sum of the deviations of a set of values $x_1$, $x_2, x_3, \ldots x_n$ measured from 100 is -20 and the algebriac sum of the deviations of the same set of values measured from 92 is 140 . If the algebraic sum of the deviations of the same set of values measured from $y$ is 180 , then what is the value of $y$ ?

  • A
    80
  • B
    85
  • Correct answer
    C
    90
  • D
    95

Solution

Here, $\left(\mathrm{x}_1-100\right)+\left(\mathrm{x}_2-100\right)+\ldots . .+\left(\mathrm{x}_{\mathrm{n}}-100\right)=-20$ hence $\left(x_1+x_2+x_3+\ldots . . x_n\right)-100 x=-20$ Or $\mathrm{x}_1+\mathrm{x}_2+\mathrm{x}_3+$ $\mathrm{x}_{\mathrm{n}}=100 \mathrm{n}-20$ and accoding to question for same set $\mathrm{x}_1+\mathrm{x}_2+\mathrm{x}_3+\ldots \ldots \ldots . . \mathrm{x}_{\mathrm{n}}=92 \mathrm{n}+140$ Acc to question $\begin{aligned} & \left(\mathrm{x}_1+\mathrm{x}_2+\mathrm{x}_3+\ldots . \mathrm{x}_{\mathrm{n}}\right)-20 \mathrm{y}=180 \\ & 1980-20 \mathrm{y}=180 \\ & \text {or } 20 \mathrm{y}=1800 \Rightarrow \mathrm{y}=90\end{aligned}$

Hence, the correct answer is option: 'C'.

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