Question

Sheela's mothers present age is 6 times her age. Sheela's age after five years from now will be one third of her mother's age. What are their present ages

Answer 1

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

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

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• Mother's present age is 6 times Sheela's age.

• Sheela's age 5 yrs from now will be one third of her mother's age.

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

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• Present ages of both.

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

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Let the mother's present age be 'x'

Let sheela's present age be 'y'

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

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$\purple\longrightarrow$ $\sf 6y = x$ -------(1)

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$\underline{\bold{\texttt{Five yrs hence age will be}}}$

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$\bf \dashrightarrow Sheela \: = \: y \: + \: 5$

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$\purple\longrightarrow$ $\sf x = 3(y + 5)$

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$\sf \longmapsto x = 3y + 15$

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$\sf \longmapsto x - 3y = 15$ --------(2)

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$\underline{\bold{\texttt{Putting x = 6y in (2)}}}$

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$\sf \longmapsto 6y - 3y = 15$

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$\sf \longmapsto 3y = 15$

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$\sf \longmapsto y = \dfrac { 15 } { 3 }$

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$\sf \longmapsto y = 5$

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$\underline{\bold{\texttt{Putting y = 5 in (1)}}}$

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$\sf \longmapsto x = 6(5)$

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$\sf \longmapsto x = 30$

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Hence present age of sheela is 5 yrs and her mother is 30 yrs old.

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$\rule{200}5$