Question

1. A 50 year old man has a son whose age is 2/5 of his
age. After how many years, the ratio of the age of the
man to his son will be 5/3?
(A) 10 years (B) 15 years (C) 20 years (D) 25 years​

Answer 1

☯ Let the old man age be x.

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$\underline{\bigstar\:\boldsymbol{According \;to \;the\: given \;Question\; :}}$

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• ${\blue{\frak{x\:=\:50\:years.}}}$

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Therefore,

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$\:\:\:\:\:\:\::\:\Longrightarrow\sf\:{His\:son\:age\:=\:{\dfrac{2}{5}}}$

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$\:\:\:\:\:\:\::\:\Longrightarrow\sf\:{\dfrac{2\:\times\:50}{5}}$

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$\:\:\:\:\:\:\::\:\Longrightarrow\sf\:{20\:years}$

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☯ Let the no. of years be y.

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$\:\:\:\:\:\:\::\:\Longrightarrow\sf\:{\dfrac{50\:+\:y}{20\:+\:y}}\:=\:{\dfrac{5}{3}}$

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$\:\:\:\:\:\:\::\:\Longrightarrow\sf\:{(50\:+\:y)3\:=\:(20\:+\:y)5}$

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$\:\:\:\:\:\:\::\:\Longrightarrow\sf\:{150\:+\:3y\:=\:100\:+\:5y}$

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$\:\:\:\:\:\:\::\:\Longrightarrow\sf\:{50\:=\:2y}$

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$\:\:\:\:\:\:\::\:\Longrightarrow\sf\:{y\:=\:{\dfrac{50}{2}}}$

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$\:\:\:\:\:\:\::\:\Longrightarrow\:{\underline{\boxed{\frak{\pink{y\:=\:25\:years}}}}}\:\bigstar$

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$\:\therefore\:{\underline{\sf{After\:{\textsf{\textbf{25\:years\:}}}\:{\sf{their\:ages\:will\:be\:in\:the\:ratio\:of\:5:3}}}}}.$

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