Question

Five years ago,anyways thrice as old as sonu after ten years ,Anu will be twice as old as sonu .how old are anu and sonu,please sent only correct answer

Answer 1

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$\Huge{\red{\underline{\textsf{Answer}}}}$

Let the present age of anu be x years.

Let the present age of sonu be y years.

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Case 1 :-

5 years ago,

Age of anu = x - 5 years.

Age of sonu = y - 5 years.

Anu was thrice as old as sonu.

$\longrightarrow$ $\sf x - 5 = 3(y - 5)$

$\longrightarrow$ $\sf x - 5 = 3y - 15$

$\longrightarrow$ $\sf x - 3y = -15 + 5$

$\orange\longrightarrow$ $\orange{\sf x - 3y = -10.....(1)}$

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Case 2 :-

10 years later,

Age of anu = x + 10

Age of sonu = y + 10

Anu will be twice as old as sonu.

$\longrightarrow$ $\sf x + 10 = 2(y + 10)$

$\longrightarrow$ $\sf x + 10 = 2y + 20$

$\longrightarrow$ $\sf x - 2y = 20 - 10$

$\green\longrightarrow$ $\green{\sf x - 2y = 10.....(2)}$

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Now in equation (1), we have

$\leadsto$ $\sf x - 3y = -10$

$\leadsto$ $\sf x = -10 + 3y$

$\textbf{Substituting \:the \:value\: of\: x\: from\: (1)\: in\: (2),}$

$\mapsto$ $\sf -10 + 3y - 2y = 10$

$\red\mapsto$ $\underline{\boxed{\red{\sf y = 20}}}$]$\orange\bigstar$

$\textbf{Putting \:the \:value\: of\: y\: in \:equation \:(1) \:we \:get,}$

$\mapsto$ $\sf x - 3(20) = -10$

$\mapsto$ $\sf x - 60 = -10$

$\pink\mapsto$ $\underline{\boxed{\pink{\sf x = 50}}}$ $\orange\bigstar$

Hence present age of sonu is 20 years and the present age of anu is 50 years.

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Answer 2

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

$\:\:$

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

$\:\:$

• Five yrs ago anu was thrice as old as sonu.

• After ten yrs Anu was twice as old as sonu.

$\:\:$

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

$\:\:$

• Ages of anu and sonu.

$\:\:$

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

$\:\:$

Let 'x' be the present age of Anu.

Let 'y' be the present age of Sonu.

$\:\:$

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

$\:\:$

$\underline{\bold{\texttt{Ages five yrs ago}}}$

$\:\:$

$\sf \dag \: Anu = x - 5$

$\:\:$

$\sf \dag \: Sonu = y - 5$

$\:\:$

Also,

$\:\:$

$\sf \longmapsto x - 5 = 3(y - 5)$

$\:\:$

$\sf \longmapsto x - 5 = 3y - 15$

$\:\:$

$\sf \longmapsto x - 3y = -15 + 5$

$\:\:$

$\sf \longmapsto x - 3y = -10$ --------(1)

$\:\:$

$\underline{\bold{\texttt{Ages ten yrs from now}}}$

$\:\:$

$\sf \dag \: Anu = x + 10$

$\:\:$

$\sf \dag \: Sonu = y + 10$

$\:\:$

Also,

$\:\:$

$\sf \longmapsto x + 10 = 2(y + 10)$

$\:\:$

$\sf \longmapsto x + 10 = 2y + 20$

$\:\:$

$\sf \longmapsto -x + 2y = -10$ --------(2)

$\:\:$

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

$\:\:$

$\sf \longmapsto -y = -20$

$\:\:$

$\sf \longmapsto \boxed {y = 20}$

$\:\:$

$\underline{\bold{\texttt{Putting y = 20 in (1)}}}$

$\:\:$

$\sf \longmapsto x - 3(20) = -10$

$\:\:$

$\sf \longmapsto x - 60 = -10$

$\:\:$

$\sf \longmapsto\boxed{ x = 50}$

$\:\:$

Hence Anu's present age is 50 years

Hence Sonu's present age is 20 years

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