Question

3 years ago father was 5 times as old as his daughter. Sevan years hence father's age is three times the age of his daughter. Find their present ages.

Answer 1

GIVEN :–

• 3 years ago father was 5 times as old as his daughter.

• Sevan years hence father's age is three times the age of his daughter.

TO FIND :–

• Their present age = ?

SOLUTION :–

• Let the age of daughter = x

• And the age of her father = y

▪︎ According to the first condition –

$\\ \implies\bf y - 3 = 5(x - 3)$

$\\ \implies\bf y - 3 = 5x -15$

$\\ \implies\bf y= 5x -12 \: \: \: \: \: \: \: - - - eq.(1)$

▪︎ According to the second condition –

$\\ \implies\bf y + 7 = 3(x + 7)$

$\\ \implies\bf y + 7 = 3x +21$

• Using eq.(1) –

$\\ \implies\bf 5x - 12+ 7 = 3x +21$

$\\ \implies\bf 5x - 5 = 3x +21$

$\\ \implies\bf 5x - 3x = 5 +21$

$\\ \implies\bf 2x = 26$

$\\ \implies\bf x = \dfrac{26}{2}$

$\\ \implies \large{ \boxed{\bf x =13}}$

• Again Using eq.(1) –

$\\ \implies\bf y= 5(13)-12$

$\\ \implies\bf y= 65-12$

$\\ \implies \large{ \boxed{\bf y=53}}$

▪︎ Hence –

• The Age of daughter = 13 year

• And The age of her father = 53 year

Answer 2

$\huge\bf{\underline{\underline{\gray{GIVEN:-}}}}$

• 3 years ago father was 5 times as old as his daughter .

• Sevan years hence father's age is three times the age of his daughter.

$\huge\bf{\underline{\underline{\gray{TO\:FIND:-}}}}$

• Their parents age .

$\huge\bf{\underline{\underline{\gray{SOLUTION:-}}}}$

Let,

• $\bf\blue{The\:age\:of\:father}$ = P

• $\bf\blue{The\:age\:of\:daughter}$ = Q

☯︎ According to the question,

ᴄᴀsᴇ - 1

${\color{aqua}\bigstar}\:\bf{\red{\overbrace{\underbrace{\green{P\:-\:3\:=\:5\:(Q\:-\:3)\:}}}}}$

⇒ P - 3 = 5Q - 15

⇒ P = 5Q - 15 + 3

⇒ P = 5Q - 12 ----(1)

ᴄᴀsᴇ - 2

$\purple\bigstar\:\bf{\pink{\overbrace{\underbrace{\blue{P\:+\:7\:=\:3\:(Q\:+\:7)\:}}}}}$

⇛ P + 7 = 3Q + 21

⇛ P = 3Q + 21 - 7

⇛ P = 3Q + 14 -----(2)

☞︎︎︎ Now comparing equation 1 & 2, we get

⇢ 5Q - 12 = 3Q + 14

⇢ 5Q - 3Q = 14 + 12

⇢ 2Q = 26

⇢ Q = 26/2

⇢ Q = 13

$\huge{\color{orange}\therefore}$ The age of the daughter is '13 years' .

☞︎︎︎ Putting the value of 'Q = 13' the equation (1), we get

➝ P = 5 × 13 - 12

➝ P = 65 - 12

➝ P = 53

$\huge{\color{orange}\therefore}$ The age of the father is '53 years' .