Question

five years hence father's age will be three times his daughter five years ago father was as old as his daughter the present ages are

Answer 1

$\large \clubs \:  \bf Correct \: Question :  -$

Five years hence Father's age will be three times his Daughter, five years ago Father was seven times as old as his Daughter. Find their Present Ages.

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$\large \clubs \:  \bf Given :  -$

• Five years hence Father's age will be three times his Daughter.

• Five years ago Father was seven times as old as his Daughter.

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$\large \clubs \:  \bf To \: Find :  -$

• Their Present Ages.

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$\large \clubs \:  \bf Solution :  -$

Let,

• Present Age of Father = x years

• Present Age of Daughter = y years

《 5 Years Hence 》

• Age of Father = (x + 5) years

• Age of Daughter = (y + 5) years

✏ According To Question :

$\red{\text{x + 5 = 3(y + 5)}}$

$:\longmapsto\text{x + 5 = 3y + 15}$

$:\longmapsto\text x = 15 - 5 +3\text y$

$:\longmapsto \bf x =3\text y+10\: - - - (1)$

《 5 Years Ago 》

• Age of Father = (x - 5) years

• Age of Daughter = (y - 5) years

✏ According To Question :

$\red{ \text{x} - 5 = 7(\text y - 5)}$

$:\longmapsto\text x - 5= 7\text y - 35$

$:\longmapsto\text x - 7\text y = - 35 + 5$

$\bf:\longmapsto x - 7y = - 30 \: - - - (2)$

✏ Putting (1) in (2) :

$3\text y + 10 - 7\text y = - 30$

$:\longmapsto \cancel- 4\text y = \cancel- 40$

$:\longmapsto\text y = \cancel\dfrac{40}{4}$

$\purple{ \Large :\longmapsto  \underline {\boxed{{\bf y = 10} }}}$

Putting Value of y in (1) :

$:\longmapsto\text x = 3 \times 10 + 10$

$:\longmapsto\text x = 30 + 10$

$\purple{ \Large :\longmapsto  \underline {\boxed{{\bf x = 40} }}}$

Hence,

$\pink{\begin{cases} \bf Age \: of \: Father = 40 \: years \\ \\ \bf Age \: of \: Daughter = 10 \: years \end{cases}}$

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Answer 2

Question

• After five years father's age will be three times his daughter and five years ago father's age was 7 times as old as his daughter. Their present ages are?

Answer

• Present age of father is 40 years.
• Present age of daughter is 10 years.

Explanation

Given that

• After 5 years father's age will he 3 times his daughter.
• And, five years ago father father's age was 7 times as old as his daughter.

To Find

• Their present ages?

Solution

• Let present age of father be m years.
• And present age of his daughter be n years.

• After five years father age will be (m + 5) years.
• And his daughter age will be (n + 5) years.

Also,

• Five years ago father age was (m - 5) years.
• And his daughter age was (n - 5) years.

❏ According to the Question :

↦ m + 5 = 3(n + 5)

↦ m = 3n + 15 - 5

➦ $\pmb{\boxed{\frak{\red{m = 3n + 10}}}}$ – – – – (1)

Also,

⇒ m - 5 = 7(n - 5)

⇒ m - 5 = 7n - 35

⇒ m = 7n - 35 + 5

➡ $\pmb{\boxed{\frak{\red{m = 7n - 30}}}}$ – – – – (2)

✇ From (1) and (2), we get :

↦ 7n - 30 = 3n + 10

↦ 7n - 3n = 10 + 30

↦ 4n = 40

↦ n = $\sf {\cancel{\dfrac{40}{4}}}$

➦ $\pmb{\boxed{\frak{\purple{n = 10}}}}$

• Therefore, present age of daughter (n) is 10 years.

¤ Putting value of 'n' in (1) :

⇒ m = 3(10) + 10

⇒ m = 30 + 10

➡ $\pmb{\boxed{\frak{\purple{m = 40}}}}$

• Therefore, present age of father (m) is 40 years.

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