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Question Number 44806 by jasno91 last updated on 05/Oct/18

Answered by Kunal12588 last updated on 05/Oct/18

let the numbers be x and y  x:y=3:5  ⇒(x/y)=(3/5)⇒x=((3y)/5)   ....(1)  (x+10):(y+10)=5:7  ⇒x=(5/7)(y+10)−10 (2)  ((3y)/5)=((5y+50−70)/7)   [from(1) and (2)]  ⇒21y=25y−100  ⇒y=25  x=3(25)/5=15     [from (1)]

$${let}\:{the}\:{numbers}\:{be}\:{x}\:{and}\:{y} \\ $$$${x}:{y}=\mathrm{3}:\mathrm{5} \\ $$$$\Rightarrow\frac{{x}}{{y}}=\frac{\mathrm{3}}{\mathrm{5}}\Rightarrow{x}=\frac{\mathrm{3}{y}}{\mathrm{5}}\:\:\:....\left(\mathrm{1}\right) \\ $$$$\left({x}+\mathrm{10}\right):\left({y}+\mathrm{10}\right)=\mathrm{5}:\mathrm{7} \\ $$$$\Rightarrow{x}=\frac{\mathrm{5}}{\mathrm{7}}\left({y}+\mathrm{10}\right)−\mathrm{10}\:\left(\mathrm{2}\right) \\ $$$$\frac{\mathrm{3}{y}}{\mathrm{5}}=\frac{\mathrm{5}{y}+\mathrm{50}−\mathrm{70}}{\mathrm{7}}\:\:\:\left[{from}\left(\mathrm{1}\right)\:{and}\:\left(\mathrm{2}\right)\right] \\ $$$$\Rightarrow\mathrm{21}{y}=\mathrm{25}{y}−\mathrm{100} \\ $$$$\Rightarrow{y}=\mathrm{25} \\ $$$${x}=\mathrm{3}\left(\mathrm{25}\right)/\mathrm{5}=\mathrm{15}\:\:\:\:\:\left[{from}\:\left(\mathrm{1}\right)\right] \\ $$

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