Question

The sum of the ages of two brothers is 24. In three years time, the elder brother will be twice as old as the younger brother. what us the present age of brothers?​

Answer 1

$\large\bf\underline \blue {To \: \mathscr{f}ind:-}$

• we need to find present Ages of both brothers.

$\huge\bf\underline \red{ \mathcal{S}olution:-}$

$\bf\underline{\purple{Given:-}}$

• Sum of ages of two brothers = 24
• After 3 years ago elder brother will be twice as old as younger brother.

${ \blue{ \mathscr{ \underline{Let : - }}}}$

• Let the age of elder brother be x years.
• Let the age of younger brother be y.

$\underline{ \large \purple{ \mathscr{\dag\:A \bf{ccourding} \: to \: \mathscr {Q} \bf{uestion} ....}}}$

Sum of ages of two brothers is 24.

$\rm \longrightarrow \:x + y = 24$

$\rm \longrightarrow \:x = 24 - y \: \: ........1)$

After 3 years ago elder brother will be twice as old as younger brother.

$\dag \underline \textbf{After three years : - }$

$\rm \leadsto \: age \: of \: younger \: brother = y + 3$

$\rm \leadsto \: age \: of \:elder \: brother =2( y + 3)$

$\rm\dashrightarrow \: x + 3 = 2( y + 3)$

$\rm\dashrightarrow \: x + 3 = 2y + 6$

$\rm\dashrightarrow \: x - 2y = 3$

• From equation ....1)

$\rm\dashrightarrow \:( 24 - y) - 2y = 3$

$\rm\dashrightarrow \: 24 - y - 2y = 3$

$\rm\dashrightarrow \: - 3y = 3 - 24$

$\rm\dashrightarrow \: -3y = - 21$

$\rm\dashrightarrow \: y = \frac{21}{3}$

$\rm\dashrightarrow \: \bf{ \pink \: y = 7}$

• Substituting value of y in ...1)

↛ x = 24 - y

↛ x = 24 - 7

↛ x = 17

Hence,

$\dag{\purple{\textbf{Age of elder brother is 17 year's}}}$

$\dag{\purple{ \textbf{Age of younger brother is 7 year's }}}$

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Answer 2

Sum of ages of two brothers is 24.

⟶x+y=24

x=24−y........1)

After 3 years ago elder brother will be twice as old as younger

After three years : -

⇝age of younger brother=y+3

⇝age of elder brother=2(y+3)

⇢x+3=2(y+3)

⇢x+3=2y+6

⇢x−2y=3

From equation ....1)

⇢(24−y)−2y=3

⇢24−y−2y=3

⇢−3y=3−24

−3y=−21

⇢y= 3/21

⇢y=7

Substituting value of y in ...1)

↛ x = 24 - y

↛ x = 24 - 7

↛ x = 17

$\dag{\purple{ \textbf{Age of elder brother is 17 year's}}}†$

$\dag{\purple{ \textbf{Age of younger brother is 7 year's }}}$