Question

when repeating decimal is 0.2323....is written in simplest form x/y then the sum of x and y is

A)23
B)99
C)122
D)NONE

optipns are given pls tell correct answer i will mark brainliest and follow​

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{0.23232323\;.\;.\;.\;.\;.\;.=\dfrac{x}{y}}$

$\underline{\textbf{To find:}}$

$\textsf{The sum of x and y}$

$\underline{\textbf{Solution:}}$

$\mathsf{Let\;\;p=0.23232323\;.\;.\;.\;.\;.\;.}$ --------(1)

$\textsf{Multiply bothsides by 100}$

$\mathsf{100\,p=23.232323\;.\;.\;.\;.\;.\;.}$ -------------(2)

$\mathsf{(2)-(1)\,\implies}$

$\mathsf{100\,p-p=23}$

$\mathsf{99\,p=23}$

$\implies\mathsf{p=\dfrac{23}{99}}$

$\textsf{As per given data, x=23 and y=99}$

$\mathsf{x+y=23+99=122}$

$\implies\boxed{\mathsf{x+y=122}}$

$\underline{\textbf{Answer:}}$

$\mathsf{Option\;(C)\;is\;correct}$