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Question Number 189363 by 073 last updated on 15/Mar/23

Answered by Rasheed.Sindhi last updated on 15/Mar/23

$$\frac{x}{y}=0.2\bar{4}$$$$100\left(\frac{x}{y}\right)=24.\bar{4}$$$$10\left(\frac{x}{y}\right)=2.\bar{4}$$$$100\left(\frac{x}{y}\right)-10\left(\frac{x}{y}\right)=22$$$$90\left(\frac{x}{y}\right)=22$$$$\frac{x}{y}=\frac{22}{90}=\frac{11}{45}=\frac{11n}{45n}$$$$x+y=11n+45n=56n$$$$min(x+y)=56\times 1=56$$$$[\because Leastpositiveinteger=1]$$

Commented by 073 last updated on 15/Mar/23

$$\mathrm{nice}\mathrm{solution}$$

Answered by BaliramKumar last updated on 15/Mar/23

$$\frac{x}{y}=0.2\bar{4}x,y\in \mathrm{N}$$$$\frac{x}{y}=\frac{24-2}{90}=\frac{22}{90}=\frac{11}{45}\mathrm{A}.\mathrm{B}\overline{\mathrm{CD}}=\frac{\mathrm{ABCD}-\mathrm{AB}}{990}$$$$min(x+y)=11+45=56$$$$$$

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