Question

Rakhi's mother is four times as old as Rakhi. After 5years, her mother will be three times as old as she will be then. Find mother's present age.

Answer 1

Answer:

${ \large{ \underline { \sf{Given}}}}$

$\: \: \: \: \: \: \: \: { \sf{❍ \: Present \: Age \: of \: Rakhi = x}}$

$\: \: \: \: \: \: \: \: { \sf{❍ \: Present \: Age \: of \: Rakhi's \: Mother=4x}}$

${ \large{ \sf{ \underline{Find}}}}$

$\: \: \: \: \: \: \: \: { \sf{❍ \:Present \: age \: of \: Rakhi's \: Mother \: age? }}$

${\large{\sf{\underline{Solution}}}}$

${\underline{ \sf{★ \: According \: to \: Question,}}}$

⇒ After 5 years, Rakhi age = 5 + x

⇒ Rakhi's mother age = 4x + 5

${\underline{ \sf{★ \: By \: Solving }}}$

$\: \: \: \: \: \: \: \: \: \: { \dashrightarrow{ \sf{4x + 5 = 3(x + 5)}}} \\ \\ \\ { \dashrightarrow{ \sf{ 4x + 5 = 3x + 15}}} \\ \\ \\ { \dashrightarrow{ \sf{4x - 3x = 15 - 5 }}} \\ \\ \\ { \dashrightarrow{ \sf{x = 10 }}} \\ \\ \\ { \boxed{ \boxed{ \sf \therefore\pink{x = 10 }}}}$

${\underline{ \sf{★ \: From \: Question,}}}$

${ \longmapsto{ \sf{Rakhi \: Mother \: Age = 4x }}} \\ \\ { \longmapsto{ \sf{Mother \: Age = 4(10) = 40}}}$

$\:$

$\:$

${ \underline{ \sf{ \underline{ \therefore{Age \: of \: Rakhi's \: Mother = 40 years}}}}}$

Answer 2

SOLUTION:-

✰ GIVEN:-

$\large{ \rightarrow}Rakhi's \: \: mother \: \: is \: \: four \: \: times \: \: as \: \: old \: \: \\ as \: \: Rakhi. \:$

✰ TO FIND:-

$\large \rightarrow \: find \: \: the \: \: Rakhi' \: \: s \: \: mother \: \: age.$

✰ SOLUTION :-

$\large \rightarrow Let \: \: the \: \: age \: \: of \: \: rakhi \: \: = \: \: x years \:$

$And \: \: according \: \: to \: \: the \: \: question \: \: it \: \: is \: \: \\ given \: \: that \: \: mother \: \: age \: \: is \: \: four \: \: times \: \: \\ the \: \: age \: \: of \: \: rakhi.$

$So \: \: the \: \: age \: \: of \: \: rakhi \: \: s \: mother \: =4x \: \: years. \: \\ \: \\ After \: \: 5 \: \: years \: \: \\ \\ </p><p>Age \: \: of \: \: rakhi \: \: = \: \: x \: + \: 5 \: \: years \: \\ \\ </p><p>Age \: \: of \: \: mother \: \: = \: \: 4 \: x \: + \: 5 \: \: years. \:$

$Now \: \: according \: \: to \: \: the \: \: second \: \: condition \: \: \\ of \: \: question \: \: after \: \: five \: \: years \: \: . Her \: \: \\ mother \: \: will \: \: be \: \: three \: \: times \: \: \: as \: \: old \: \: \\ as rakhi. \:$

$⇒4x+5= 3(x+5) \\ \\ </p><p></p><p>⇒4x+5= 3x + 15 \\ \\ ⇒ 4x -3x = 15-5 \: \\ \\ \: therefore \: x \: =10$

$Hence \: \: the \: \: present \: \: age \: \: of \: \: rakhi \: \: = x \\ \: years \: =10 \: \: years \: \: \\ \\and \:\\ \\ the \: \: age \: \: of \: \: Rakhi \: mother= 4x years = \: the \: \: age \: \: of \: Rakhi \: s \\ ×10=404×10=40 \: years \:$

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