Question

Deepak’s present age is one-third his mother’s present age. If the mother’s age was five times
his age 6 years ago, what are Mom & Son’s present ages?

Answer 1

Given that , Deepak’s present age is one-third his mother’s present age and 6 years ago his mother’s age was five times of Deepak's age .

Exigency To Find : Present age of Deepak and his mother ??

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀

❍ Let's say that , Present age of her mother be x yrs & Deepak's Present age be ⅓ × x yrs i.e., Deepak’s present age is one-third his mother’s present age .

$\\\qquad \bigstar \:\:\underline {\pmb{\sf {\purple { \:According \:To \:The \:Question \::\:}}}}$

⠀⠀⠀━━⠀6 years ago his mother’s age was five times of Deepak's age .

$\\\qquad \dashrightarrow \sf \: \:\Big\{ \:Mothers's \:Age \:-\:6\:\Big\}\:=\:5\;\Big\{ \:Deepak's \:Age \:-\:6\:\Big\} \\\\\\\qquad \dashrightarrow \sf \: \:\Big\{ \:x \:-\:6\:\Big\}\:=\:5\;\bigg\{ \:\dfrac{1}{3}\:\times\:x \:-\:6\:\bigg\} \\\\\\ \qquad \dashrightarrow \sf \: \:\Big\{ \:x \:-\:6\:\Big\}\:=\:5\;\bigg\{ \:\dfrac{x}{3}\: \:-\:6\:\bigg\} \\\\\\ \qquad \dashrightarrow \sf \: \:\Big\{ \:x \:-\:6\:\Big\}\:=\:\;\bigg\{ \:\dfrac{5x}{3}\: \:-\:30\:\bigg\} \\\\\\ \qquad \dashrightarrow \sf \: \:\;\bigg\{ \:\dfrac{5x}{3}\: \:-\:x\:\bigg\} \:\:=\:-6\:+\:30\: \\\\\\ \qquad \dashrightarrow \sf \: \:\;\bigg\{ \:\dfrac{5x}{3}\: \:-\:x\:\bigg\} \:\:=\:24\: \\\\\\ \qquad \dashrightarrow \sf \: \:\;\bigg\{ \:\dfrac{5x\:-\:3x}{3}\: \:\bigg\} \:\:=\:24\: \\\\\ \qquad \dashrightarrow \sf \: \:\;\bigg\{ \:\dfrac{2x}{3}\: \:\bigg\} \:\:=\:24\: \\\\\\ \qquad \dashrightarrow \sf \: \:\;2x\: \: \:\:=\:24\:\times \:3\: \\\\\\ \qquad \dashrightarrow \sf \: \:\;2x\: \: \:\:=\:72\: \\\\\\ \qquad \dashrightarrow \sf \: \:\;x\: \: \:\:=\:\cancel{\dfrac{72}{2}}\: \\\\\\ \qquad \dashrightarrow \underline {\boxed {\pmb{\frak{ \: x\: \: \:\:=\:36\:yrs\;}}}}\:\:\bigstar$

Therefore,

• Mother’s present age is : x = 36 yrs &
• Deepak’s present age is : ⅓ × x = ⅓ × 36 = 12 yrs .

$\qquad \therefore \:\underline {\sf \:Hence, \:Present \:ages \:of \:Deepak\:and \:his \:mother \:are \:\pmb{\bf 12 \:yrs\:} and \:\pmb{\bf 36 \:yrs \:}\:,respectively\:.}$