Question

A is 15 years older than B. Ten years ago, A was four times B's age. What are their ages now? ​

Answer 1

Given that , A is 15 years older than B & Ten years ago , A was four times B's age.

Need To Find : A's and B's Present ages ?

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❍ Let's , say that B's Present age be x yrs & A's Present age be ( x + 15 ) yrs , i.e. A is 15 years older than B .

$\qquad \bigstar \:\:\underline {\purple {\pmb{\sf \:According \:to\:the\:Given \:Question \:\::\:}}}$

⠀⠀━━━ Ten years ago , A's age was four times of B's age.

$\\ \qquad \dashrightarrow \sf\: \Big\{ A's \:age \: -\:10\:\Big\}\:=\:4\:\Big\{ B's \:age \: -\:10\:\Big\}\:\\\\\\ \qquad \dashrightarrow \sf\: \Big\{ \big( x + 15 \big) \: \: -\:10\:\Big\}\:=\:4\:\Big\{ x \: -\:10\:\Big\}\:\\\\\\ \qquad \dashrightarrow \sf\: \Big\{ x + 15 \: -\:10\:\Big\}\:=\:4\:\Big\{ x \: -\:10\:\Big\}\:\\\\\\ \qquad \dashrightarrow \sf\: \Big\{ x + 5 \: \:\Big\}\:=\:\:\Big\{ 4x \: -\:40\:\Big\}\:\\\\\\ \qquad \dashrightarrow \sf\: x + 5 \: \:\:=\:\: 4x \: -\:40\:\:\\\\\\ \qquad \dashrightarrow \sf\: 3x \: \:\:=\:\:\:45\:\:\\\\\\ \qquad \dashrightarrow \sf\: x \: \:\:=\:\:\dfrac{45}{3}\:\:\\\\\\ \qquad \dashrightarrow \underline {\boxed {\pmb{\frak{\purple {\: x \: \:\:=\:\:\:15\:yrs\:}}}}} \:\:\bigstar$

Therefore,

• A's Present age will be : ( x + 15 ) = ( 15 + 15 ) = 30 yrs &,
• B's Present age will be : x = 15 yrs .

$\\\therefore \:\underline {\sf Hence, \:The \:A's \:and \:B's \:Present \:ages \:are\:\:\pmb{\bf\: 30 \:yrs \:\&\:15\:yrs \:}\:,respectively\:.}$