Question

20 years ago the age of a father was four times the age of his son. After four years
from now the age of father will be double that of the son. Find the present ages of the
father and son

Answer 1

Given that:

• 20 years ago the age of a father was four times the age of his son.
• After four years from now the age of father will be double that of the son.

To Find:

• The present ages of the father and son.

Let us assume:

• The present age of son be x.
• And the present age of father be y.

20 years ago:

• Son's age = x - 20
• Father's age = y - 20

According to the question.

↠ 4(x - 20) = y - 20

↠ 4x - 80 = y - 20

↠ 4x - 80 + 20 = y

↠ 4x - 60 = y (i)

After four years:

• Son's age = x + 4
• Father's age = y + 4

According to the question.

↠ 2(x + 4) = y + 4

↠ 2x + 8 = y + 4

↠ 2x + 8 - 4 = y

↠ 2x + 4 = y (ii)

Comparing eqⁿ (i) and eqⁿ (ii):

↣ 4x - 60 = 2x + 4

↣ 4x - 2x = 4 + 60

↣ 2x = 64

↣ x = 64/2

↣ x = 32

Putting the value of x in eqⁿ (ii):

↣ 2x + 4 = y

↣ 2(32) + 4 = y

↣ 64 + 4 = y

↣ 68 = y

↣ y = 68

Hence,

The present ages of:

• Son = 32 years
• Father = 68 years

Answer 2

Answer :-

$\quad\pink{\bigstar}\:\sf Present \:age \:of\: son\:\leadsto\:{\boxed{\tt{\blue{32\:years}}}}$

$\quad\pink{\bigstar}\:\sf Present \:age \:of\: father\:\leadsto\:{\boxed{\tt{\blue{68\:years}}}}$

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\linethickness{3mm}\put(1,1){\line(1,0){6.8}}\end{picture}$

• Given :-

• 20 years ago the age of a father was four times the age of his son.

• After four years from now the age of father will be double that of the son.

• To Find :-

• Present ages of son and father = ?

• Solution :-

• Let present age of son be m

• And present age of father be n

$\bf\dag\:{\underline{\sf{20\:years\:ago\::}}}$

• Age of son = (m - 20) years

• Age of father = (n - 20) yearss

A/q,

➪ Age of father = 4 × (Age of his son)

➪ n - 20 = 4 × (m - 20)

➪ n - 20 = (4 × m) - (4 × 20)

➪ n - 20 = 4m - 80

➪ n = 4m - 80 + 20

$\bigstar\:\underline{\underline{\bf{\red{n = 4m - 60}}}}\:\dashrightarrow\:{\bf{\green{[eq^{n}\:(1)]}}}$

$\bf\dag\:{\underline{\sf{After\:4\:years\::}}}$

• Age of son = (m + 4) years

• Age of father = (n + 4) years

A/q,

➪ Age of father = 2 × (Age of his son)

➪ n + 4 = 2 × (m + 4)

➪ n + 4 = (2 × m) + (2 × 4)

➪ n + 4 = 2m + 8

➪ n = 2m + 8 - 4

$\bigstar\:\underline{\underline{\bf{\red{n = 2m + 4}}}}\:\dashrightarrow\:{\bf{\green{[eq^{n}\:(2)]}}}$

⌬ From [eqⁿ (1)] and [eqⁿ (2)], we get :-

➪ 4m - 60 = 2m + 4

➪ 4m - 2m = 4 + 60

➪ 2m = 64

➪ m = 64/2

$\bigstar\:\underline{\underline{\bf{\red{m = 32}}}}$

⌬ Putting value of "m" in [eqⁿ (1)] :-

➪ n = (4 × 32) - 60

➪ n = 128 - 60

$\bigstar\:\underline{\underline{\bf{\red{n = 68}}}}$

Hence,

• Present age of son = 32 years

• Present age of father = 68 years

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