Question

The age of A is one-third of the age of B. After 15 years,The age of A will
be half of the age of B. Find their present ages.

Answer 1

A present age s 15
B present age s 45

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

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$\green{\underline \bold{Given :}}$

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• The age of 'A' is one third of the age of 'B'

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• After 15 years the age of 'A' will be half of the age of 'B'

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$\red{\underline \bold{To \: Find:}}$

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• Their present ages

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$\large{\orange{\underline{\tt{Solution :-}}}}$

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Let the present age of 'A' be x

Let the present age of 'B' be y

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$\purple{\underline \bold{According \: to \: the \ question :}}$

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$\purple\longrightarrow$ $\sf x = \dfrac { 1 } { 3 } y$

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$\sf \longmapsto 3x = y$

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$\sf \longmapsto y - 3x = 0$

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$\sf \longmapsto -3x + y = 0$ ------(1)

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$\underline{\bold{\texttt{After 15 yrs ages will be :}}}$

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a' age = x + 15

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b's age = y + 15

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So,

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$\purple\longrightarrow$ $\sf x + 15 = \dfrac { 1 } { 2 }\times (y + 15)$

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$\sf \longmapsto x + 15 = \dfrac { y + 15 } { 2 }$

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$\sf \longmapsto 2x + 30 = y + 15$

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$\sf \longmapsto 2x - y = 15 - 30$

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$\sf \longmapsto 2x - y = - 15$ -------(2)

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$\underline{\bold{\texttt{Adding (1) \& (2)}}}$

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$\sf \longmapsto -3x + 2x + y - y = 0 - 15$

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$\sf \longmapsto -x = -15$

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$\bf \dashrightarrow x = 15$

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$\underline{\bold{\texttt{Putting x = 15 in (2)}}}$

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$\sf \longmapsto 2(15) - y = - 15$

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$\sf \longmapsto 30 - y = - 15$

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$\sf \longmapsto y = 30 + 15$

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$\bf \dashrightarrow y = 45$

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Hence 'A' is 15 yrs old & 'B' is 45 yrs old.

$\rule{200}5$