Question

the ages of A and B arebin the ratio 3:5. If after 5 yrs their ages will be in the ratio 2:3 , then the present age of B in years​

Answer 1

$\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}$

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$\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$

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• Ages of A and B are in the ratio 3:5

• After 5 yrs their ages will be in the ratio 2:3

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$\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$

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• Present age of B in years

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$\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$

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Given that the ages of A and B are in the ratio 3:5

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So,

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Let the present age of A be "3p"

Let the present age of B be "5p"

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$\underline{\bold{\texttt{A's age after 5 years :}}}$

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➠ 3p + 5 ⚊⚊⚊⚊ ⓵

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$\underline{\bold{\texttt{B's age after 5 years :}}}$

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➠ 5p + 5 ⚊⚊⚊⚊ ⓶

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$\rm{ \large{\pink{\underline\blue{According \: to \: the \ question :}}}}$

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After 5 yrs their ages will be in the ratio 2:3

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From ⓵ & ⓶

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➜ $\sf \dfrac { 3p + 5 } { 5p + 5 } = \dfrac { 2 } { 3 }$

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➜ 3(3p + 5) = 2(5p + 5)

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➜ 9p + 15 = 10p + 10

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➜ 10p - 9p = 15 - 10

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➜ p = 5

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We assumed B's present age to be 5p

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Thus ,

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$\underline{\bold{\texttt{B's present age :}}}$

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➜ 5p

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➜ 5(5)

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➨ 25

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• Hence the present age of B is 25 years