Question

Sum of ages of father and son is 68 years After 8 years father will b thrice older than son .What is the present sons age ?

Answer 1

${\bf{Given\::}}$

• Sum of ages of father and son is 68 years.

• After 8 years father will be thrice older than son.

$\\ {\bf{To\: Find\::}}$

• The present age of son.

$\\ {\bf{Solution\::}}$

Let,

⑴ Present of father is x years.

And

⑵ Present age of his son is y years.

★ It is given that, sum of ages of father and son is 68 years.

$:\implies\:\bf{x\:+\:y\:=\:68}$

$:\implies\:{\Large\mid}\:\bf{x\:=\:68\:-\:y}\:{\Large\mid}---(1)$

☛ After 8 years,

➛ Father's age = (x + 8) years

And

➛ His sons age = (y + 8) years

★ It is given that, after 8 years father will be thrice older than his son.

$:\implies\:\bf{(x\:+\:8)\:=\:3\times{(y\:+\:8)}}$

➳ x + 8 = 3y + 24

☛ Putting the value of x from equation (1), we get

➳ 68 - y + 8 = 3y + 24

➳ 3y + y = 76 - 24

➳ 4y = 52

➳ y = $\tt{\dfrac{52}{4}}$

➳ y = $\bf\pink{13}$

∴ The present age of his son is 13 years.

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☛ Putting the value of y in equation (1), we get

➳ x = 68 - y

➳ x = 68 - 13

➳ x = 55

∴ The present age of father is 55 years.

Answer 2

Given:

• The sum of ages of the father and the son is 68 years. After eight years, father will be thrice as old as his son.

To find:

• Present age of the son.

Solution: Let the present age of father be x years and the son be y years respectively.

A/Q,

• Case : I) The sum of ages of the father and the son is 68 years.

➠ x + y = 68

➠ x = 68 - y ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀—eq(I).

• Case : II) After eight years, father will be thrice as old as his son.
• Father's age = (x + 8) & Son's age = (y + 8)

★ Age of father = 3 × (Age of son) ★

$\implies$ (x + 8) = 3(y + 8)

$\implies$ x + 8 = 3y + 24

$\implies$ x = 3y + 24 - 8

$\implies$ x = 3y + 16⠀⠀—eq(II).

• By using Both equations, (I) & (II).

$\implies$ 68 - y = 3y + 16

$\implies$ 68 - 16 = 3y + y

$\implies$ 52 = 4y

$\implies$ y = 52/4

$\implies$ y = 13 ★

• Substituting the value of 'y' in equation (I).

➠ x = 68 - y ⠀

➠ x = 68 - 13

➠ x = 55 ★

•°• Hence, the present age of son and father are 13 years and 55 years respectively.

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★ VERIFICATION :

• We're given with the sum of the ages of father and son that is 68 years. Let's verify the ages of father and son. Therefore,

➠ (Father's age) + (Son's age) = 68

➠ 55 + 13 = 68

➠ 68 = 68

⠀⠀⠀⠀⠀$\therefore$ Hence Verified!