Question

The present age of Monu is 1/5 times his mother's age. After 5 year his age will be 1/3 times his mother's age of that time. find their present age.​

Answer 1

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Answer 2

Given : The present age of Monu is ⅕ times his mother's age and After 5 year his age will be ⅓ times his mother's age .

Need To Find : Present age Monu and his mother ?

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❍ Let's say that , Mother’s age be x yrs & Monu's age be ( ⅕ × x ) yrs i.e, The present age of Monu is ⅕ times his mother's age .

⠀⠀⠀☯︎ After 5 years their Ages :

• Mother's age will be : ( x + 5 ) yrs &
• Monu's age will be : ( ⅕ × x + 5 ) yrs .

$\\\qquad \star\:\underline {\pmb{\frak{ According \:To \:The\:Given \:Question \:\::\:}}}$

⠀▪︎⠀After 5 year Monu's age will be ⅓ times his mother's age .

$\\\\:\implies \sf \Big\{ Monu's \:Age\:_{\:(After \:5\:Years )\:}\:\Big\}\:=\:\dfrac{1}{3}\:\Big\{ Mother's \:Age\:_{\:(After \:5\:Years )\:}\:\Big\}\:\:$

$:\implies \sf \bigg\{\:\dfrac{1}{5}\times x\:+\:5 \:\bigg\}\:=\:\dfrac{1}{3}\:\bigg\{ x + 5\:\:\bigg\}\:\:$

$:\implies \sf \bigg\{\:\dfrac{x}{5}\:+\:5 \:\bigg\}\:=\:\bigg\{ \dfrac{x}{3} + \dfrac{5}{3}\:\bigg\}\:\:$

$:\implies \sf \:\dfrac{x}{5}\:+\:5 \:\:=\:\dfrac{x}{3} + \dfrac{5}{3} \:\:$

$:\implies \sf \:\dfrac{x}{5}\:-\:\dfrac{x}{3} \:\:=\:\dfrac{5}{3} -\:5\:$

$:\implies \sf \:\dfrac{3x - 5x}{15} \:\:=\:\dfrac{5- 15}{3}\:$

$:\implies \sf \:-\dfrac{2x}{15} \:\:=\:-\dfrac{10}{3}\:$

$:\implies \sf \:\dfrac{2x}{15} \:\:=\:\dfrac{10}{3}\:\qquad \bigg\lgroup Canceling \:\pmb{\sf{-ve\:}}\:sign\:\bigg\rgroup$

$:\implies \sf \dfrac{x}{15} \:\:=\:\dfrac{10}{3\times 2 }\:$

$:\implies \sf x \:\:=\:\dfrac{10 \times 15 }{3\times 2 }\:$

$:\implies \sf x \:\:=\:\cancel {\dfrac{150 }{6 }}\:$

$:\implies \pmb {\underline {\boxed {\purple {\:\frak{ \:x\:\:=\:25\:yrs\:}}}}}\:\bigstar \:$

Therefore,

• Mother's age , x = 25 yrs &
• Monu's age , ( ⅕ × x ) = [ ⅕ × 25 ] = 5 yrs

$\therefore \underline {\sf \: Hence, \:Present \:ages \:of \: Monu\:and\:his\:mother \:are\:\pmb{\sf 5\:yrs\:\&\:25\:yrs\:}\:,\:respectively \:.}$