Question

The age of michel and andy are in ratio 9:4 seven years hence ratio of their ages will be 5:3. Find their present ages....​

Answer 1

Answer:

The present age of Michael = 18 years

The present age of Andy = 8 years

Step-by-step explanation:

Given :

• The ages of Michael and Andy are in ratio 9:4
• Seven years hence ratio of their ages will be 5:3

To find :

their present ages

Solution :

Since their present ages are in the ratio 9 : 4, let

the present age of Michael be 9x

and the present age of Andy be 4x

After 7 years,

Michael's age = (9x + 7) years

Andy's age = (4x + 7) years

As given,

  $\tt \dfrac{9x+7}{4x+7}=\dfrac{5}{3} \\\\ \tt 3(9x+7)=5(4x+7) \\\\ \tt 27x+21=20x+35 \\\\ \tt 27x-20x=35-21 \\\\ \tt 7x=14 \\\\ \tt x=14/7 \\\\ \tt x=2$

The present age of Michael = 9(2) = 18 years

The present age of Andy = 4(2) = 8 years

Verification :

• The present age of Michael = 18 years

• The present age of Andy = 8 years

Condition - 1 :

Their ages are in the ratio 9 : 4

 18 : 8 = 9 : 4

 2(9) : 2(4) = 9 : 4

   9 : 4 = 9 : 4

  LHS = RHS

Condition - 2 : Seven years hence ratio of their ages will be 5:3

After seven years,

Michael's age = 18+7 = 25

Andy's age = 8+7 = 15

 25 : 15 = 5 : 3

 5(5) : 5(3) = 5 : 3

  5 : 3 = 5 : 3

  LHS = RHS

Hence verified!

Answer 2

$\large \bigstar{ \underline{ \underline{ \bf \red{ ConCepT}}}} \bigstar\leadsto$

$\small \bf Here \: in \: this \: Question, We \: have \: to \: \\ \small \bf find \: out \: the \: present \: age \: of \: Michael \\ \small \bf and \: Andy \: if \: their \: ages \: are\: in \: the \\ \small \bf\: ratio \: of \: 9:4 \: and \: After \: seven \: years \: \\ \small \bf their \: ages \: will \: be \: in \: the \: ratio \: of \: 5:3.$

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$\large \bigstar{ \underline{ \underline{ \bf \blue{ GiVeN}}}} \bigstar\leadsto$

• $\small \bf The \: ages \: of \: Michael \: and \: \: Andy \\ \small \bf are\: in \: the \: ratio \: of \: 9:4 \:$

• $\small \bf After \: seven \: years \: the \: ages \: of \\ \small \bf\: Michael \: and \: Andy \: will \: be \\ \small \bf\: in \: the \: ratio \: of \: 5:3.$

══════ •『 ♡ 』• ══════

$\large \bigstar{ \underline{ \underline{ \bf \pink{ To \: FinD}}}} \bigstar\leadsto$

• $\small \bf \: The \: Present \: age \: of \: Michael \\ \small \bf and \: Andy$

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$\large \bigstar{ \underline{ \underline{ \bf \green{ SoLuTioN}}}} \bigstar\leadsto$

$\small \bf \: Let,$

$\small \bf \:\\ \small \bf \pink\bigstar the \: present \: age \: of \: Michael \: be \: 9x \\ \small \green\bigstar \bf the \: present \: age \: of \: Andy \: be \: 4x \: \: \: \: \:$

$\small \bf \underline{After \: 7 \: years,}$

$\small \bf \color{lime}{\bigstar }\: \color{navy} {Michael's \: age \: will \: be \longrightarrow \boxed{ \sf \green{ (9x + 7)}}}$

$\small \bf \color{lime}{\bigstar }\: \color{navy} {Andy's \: age \: will \: be \longrightarrow \boxed{ \sf \green{ (4x + 7)}}}$

$⟹ \bf\: \frac{(9x + 7)}{(4x + 7)} = \frac{5}{3}$

$⟹ \bf\: 3(9x + 7) = 5(4x + 7)$

$⟹ \bf\: 27x + 21 = 20x + 35$

$⟹ \bf\: 27x - 20x = 35 - 21$

$⟹ \bf\: 7x = 14$

$⟹ \bf\: x = \frac{ \cancel{14}} {\cancel{2} }$

$⟹ \bf\: x = 2$

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$\bf\therefore \small \bf \color{brown}{\bigstar }\: \color{darkgreen} {Michael's \: present \: age \: will \: be \pink \leadsto \red {9x}} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \small \leadsto \bf 9 \times 2 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \small \bf \leadsto 18$

$\bf\therefore \small \bf \color{brown}{\bigstar }\: \color{darkgreen} {Andy's \: present \: age \: will \: be \pink \leadsto \red {4x}} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \small \leadsto \bf 4 \times 2 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \small \bf \leadsto 88$

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$\\ \bigstar{ \underline{ \underline \pink{ \sf★@iTzShInNy☆}}} \bigstar$

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