Question

18 years ago, a woman was three times as old as her daughter. Now, the woman is twice as old as her daughter. The sum of the present ages of the woman and her daughter is

Answer 1

Given : A woman is twice as old as her daughter & 18 years ago, a woman was three times as old as her daughter .

Need To Find : The sum of Woman's and Daughter's Present age ?

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❍ Let's say , that age of Daughter be x years & age of Woman be 2x years , i.e. Woman is twice as old as her daughter .

⠀☆ 18 years ago their ages :

• Woman's age will be : ( 2x - 18 ) years &
• Daughter's age will be : ( x - 18 ) years .

$\\\dag \:\underline {\pmb{\frak { According \:To\:the\:\:Given \:\:Question \::\:}}}$

⠀⠀▪︎⠀⠀18 years ago, a woman was three times as old as her daughter .

$\\:\implies \sf \Big\{ Woman's_{\:(Age)\:}\:\Big\} \:=\:3\:\Big\{ Daughter's_{\:(Age)\:}\:\Big\}\:$

$:\implies \sf \Big\{ \:2x - 18\:\Big\} \:=\:3\:\Big\{ \: x - 18\:\Big\}\:$

$:\implies \sf \:2x - 18\: \:=\:\: \: 3x - 54\:\:$

$:\implies \sf \:2x - 3x\: \:=\: - 54 + 18\:\:$

$:\implies \sf \:-x\: \:=\: -36\:\:$

$:\implies \sf \:x\: \:=\:36\:\qquad \Bigg\lgroup \: Eliminating \:\pmb{\sf -ve\:}\:sign\:\Bigg\rgroup \:$

$:\implies \pmb{\sf \:x\: \:=\:36\:years }\:\:$

Therefore,

• Woman's age , 2x = 2 × 36 = 72 years &
• Daughter's age , x = 36 years .

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$\qquad \dag\underline {\pmb{\frak{ \: The \:Sum \:of \:their \:ages \:\::\:}}}$

$\dashrightarrow \sf Sum\:_{\:( Age's)\:}\:=\:\Big\{ Woman's\:Age\:\Big\}\:+\:\:\Big\{ Daughter's \:Age\:\Big\}\:\\\\\\\dashrightarrow \sf Sum\:_{\:( Age's)\:}\:=\:\Big\{ 72 \:\Big\}\:+\:\:\Big\{ 36\:\Big\}\:\\\\\\ \dashrightarrow \sf Sum\:_{\:( Age's)\:}\:=\: 72\:\:+\: 36\:\\\\\\\dashrightarrow \pmb {\underline {\boxed {\purple {\:\frak{ \:Sum_{\:(Age's)\:}\:\:=\:108\:years \:}}}}}\:\bigstar \:$

$\therefore \:\underline {\sf Hence, \:The\:Sum\:of\:their\:Present \:age's\:is\:\pmb{\sf 108\:years \:}\:.}$

Answer 2

Answer:

Eighteen years ago, a mother was three times as old as her daughter. Now the mother is only twice as old as her daughter. Then the sum of the present ages ...

Explanation: