Question Number 189363 by 073 last updated on 15/Mar/23
Answered by Rasheed.Sindhi last updated on 15/Mar/23
![(x/y)=0.24^(−) 100((x/y))=24.4^(−) 10((x/y))=2.4^(−) 100((x/y))−10((x/y))=22 90((x/y))=22 (x/y)=((22)/(90))=((11)/(45))=((11n)/(45n)) x+y=11n+45n=56n min(x+y)=56×1=56 [∵ Least positive integer=1]](https://www.tinkutara.com/question/Q189364.png)
$$\frac{{x}}{{y}}=\mathrm{0}.\mathrm{2}\overline {\mathrm{4}} \\ $$$$\mathrm{100}\left(\frac{{x}}{{y}}\right)=\mathrm{24}.\overline {\mathrm{4}} \\ $$$$\mathrm{10}\left(\frac{{x}}{{y}}\right)=\mathrm{2}.\overline {\mathrm{4}} \\ $$$$\mathrm{100}\left(\frac{{x}}{{y}}\right)−\mathrm{10}\left(\frac{{x}}{{y}}\right)=\mathrm{22} \\ $$$$\mathrm{90}\left(\frac{{x}}{{y}}\right)=\mathrm{22} \\ $$$$\frac{{x}}{{y}}=\frac{\mathrm{22}}{\mathrm{90}}=\frac{\mathrm{11}}{\mathrm{45}}=\frac{\mathrm{11}{n}}{\mathrm{45}{n}} \\ $$$${x}+{y}=\mathrm{11}{n}+\mathrm{45}{n}=\mathrm{56}{n} \\ $$$${min}\left({x}+{y}\right)=\mathrm{56}×\mathrm{1}=\mathrm{56} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left[\because\:{Least}\:{positive}\:{integer}=\mathrm{1}\right] \\ $$
Commented by 073 last updated on 15/Mar/23
$$\mathrm{nice}\:\mathrm{solution} \\ $$
Answered by BaliramKumar last updated on 15/Mar/23
$$\frac{{x}}{{y}}\:=\:\mathrm{0}.\mathrm{2}\overline {\mathrm{4}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x},\:{y}\:\in\:\mathrm{N} \\ $$$$\frac{{x}}{{y}}\:=\:\frac{\mathrm{24}−\mathrm{2}}{\mathrm{90}}\:=\:\frac{\mathrm{22}}{\mathrm{90}}\:=\:\frac{\mathrm{11}}{\mathrm{45}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{A}.\mathrm{B}\overline {\mathrm{CD}\:}\:=\:\frac{\mathrm{ABCD}−\mathrm{AB}}{\mathrm{990}} \\ $$$${min}\left({x}+{y}\right)\:=\:\mathrm{11}+\mathrm{45}\:=\:\mathrm{56} \\ $$$$ \\ $$