Question

Present age of Sumitra is twice the present age of Sulekha . 10 yeras ago, the age of Sumitra was thrice the age of Sulekha . What are their present ages ?​

Answer 1

$\huge\bf\red{\underline{\underline{Given}}}\::$

• ${\sf{\gray{Present \:age\: of \:Sumitra\: is\:}}}{\sf{\pink{twice}}}{\sf{\gray{\:the\: present \:age\: of \:Sulekha}}}$

• ${\sf{\green{10 \:yeras\: ago,}}}{\sf{\gray{\:The \:age \:of \:Sumitra\: was}}}{\sf{\pink{\:thrice}}}{\sf{\gray{\:the\: age \:of\: Sulekha.}}}$

$\huge\bf\red{\underline{\underline{To\:Find}}}\::$

• ${\sf{\gray{Present\:ages\:of\:}}}{\sf{\blue{Sumitra}}}\:{\sf{\gray{\&}}}\:{\sf{\purple{Sulekha}}}$

$\huge\bf\red{\underline{\underline{Solution}}}\::$

$\:\:\:\star\:\bf\orange{Let\:} \begin{cases}{\sf{\green{\:\:Present\:age\:of\:Sulekha}}}{\sf{\:=\:}}{\sf{\red{x \: years}}}\\\\ {\sf{\green{\:\:Present\:age\:of\:Sumitra}}}{\sf{\:=\:}}{\sf{\red{2x \: years}}}\\ \end{cases}$

◼ $\sf\underline\red{10\:years\:ago}$

${\sf{\purple{Age\:of\:Sulekha}}}\:{\sf{\:=\:}}\:{\sf{\orange{x\:-\:10\:years}}}$

${\sf{\blue{Age\:of\:Sumitra}}}\:{\sf{\:=\:}}\:{\sf{\orange{2x\:-\:10\:years}}}$

$\:\:\:\:\:\hookrightarrow\:{\sf{\green{2x\:-\:10}}}\:{\sf{=\:}}{\sf{\pink{2(x\:-\:10)}}}$

$\:\:\:\:\:\hookrightarrow\:{\sf{\purple{2x\:-\:10}}}\:{\sf{=\:}}{\sf{\pink{3x\:-\:30}}}$

$\:\:\:\:\:\hookrightarrow\:{\sf{\green{x}}}\:{\sf{=\:}}{\sf{\pink{20}}}$

$\:\:\:\:\:\hookrightarrow\:{\sf{\purple{2x}}}\:{\sf{=\:}}{\sf{\pink{40}}}$

$\star\:\sf\underline\red{Present \:age\: of \: Sulekha\:=\:20\:years}$

$\star\:\sf\underline\red{Present \:age\: of \: Sumitra\:=\:40\:years}$

Answer 2

$\orange{\large{\underline{\underline{ \rm{Given: }}}}}$

◕ Present age of Sumitra is twice the present age of Sulekha.

◕ 10 years ago, the age of Sumitra was thrice the age of Sulekha.

$\orange{\large{\underline{\underline{ \rm{To \: Find: }}}}}$

◉ Their present ages.

$\orange{\large{\underline{\underline{ \rm{Let's \: Find \: out: }}}}}$

Let the present age of Sulekha = x

∴ Present age of Sumitra = 2x

10 years ago,

(To find the ten years ago and we will subtract 10 from their ages.)

Age of Sulekha = (x - 10) years

Age of Sumitra = (2x - 10) years

According to the problem:-

2x - 10 = 3(x - 10)

On solving :-

2x -10 = 3x - 30

- 10 + 30 = 3x - 2x

$\green{ \underline{ \boxed{ \gray{ \rm{ x = 20}}}}}$

∴ Present age of Sulekha = $\green{ \underline{ \boxed{ \gray{ \rm{ 20 \: years}}}}}$

and,

Present age of Sumitra =$\gray{ \rm{2 \times 20 \: = {\green{ \underline{ \boxed{ \gray{ \rm{40 \: years}}}}}}}}$

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