Question

Sum of Ages of father and son is 74 after 8 years father will be twice as old as son the present age in years of the father is

Answer 1

Given:

• The sum of ages of the father and the son is 74 years.
• After eight years, father will be twice as old as his son.

To find:

• Present age of the father.

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 74 years.

➠ x + y = 74

➠ x = 74 - y ⠀⠀⠀⠀⠀⠀ —eq(I).

• Case : II) After eight years, father will be twice as old as his son.

• Father's age = (x + 8) and Son's age = (y + 8)

★ Age of father = 2 × (Age of son) ★

➠ (x + 8) = 2 × (y + 8)

➠ x + 8 = 2y + 16

➠ x = 2y + 16 - 8

➠ x = 2y + 8 ⠀⠀⠀⠀⠀⠀ —eq(II).

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

$\implies$ 74 - y = 2y + 8

$\implies$ 74 - 8 = 2y + y

$\implies$ 66 = 3y

$\implies$ y = 66/3

$\implies$ y = 22 ★

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

$\implies$ x = 74 - y

$\implies$ x = 74 - 22

$\implies$ x = 52 ★

•°• Hence, the present age of father and son are 52 years and 22 years respectively.

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★ VERIFICATION :

• We're given with the sum of the ages of father and son that is 74 years. Let's verify the ages of father and son.

➠ (Father's age) + (Son's age) = 74

➠ 52 + 22 = 74

➠ 74 = 74

⠀⠀⠀⠀⠀$\therefore$ Hence Verified!

Answer 2

Question:-

Sum of Ages of father and son is 74 after 8 years father will be twice as old as son the present age in years of the father is ?

To Find:-

Find the present age of father.

Solution:-

Here ,

The sum of father's age and sons age is

$\tt\implies \: x + y = 74$

$\tt\implies \: x = 74 - y . . . . . . ( 1 )$

After 8 years father will be twice old as son.

$\tt\implies \: Father's \: \: age = 2( x + 8 )$

$\tt\implies \: Sons \: \: age = ( y + 8 )$

According to Question:-

$\tt\implies \: Age \: \: of \: \: father = 2 × ( Age \: \: of \: \: son )$

$\tt\implies \: ( x + 8 ) = 2( y + 8 )$

$\tt\implies \: x + 8 = 2y + 16$

$\tt\implies \: x = 2y + 16 - 8$

$\tt\implies \: x = 2y + 8$

Substitute " x " in equation ( 1 ):-

$\tt\implies \: 74 - y = 2y + 8$

$\tt\implies \: 74 - 8 = 2y + y$

$\tt\implies \: 3y = 66$

$\tt\implies \: y = 22 \: years$

Then ,

Father's age =

$\tt\implies \: x = 74 - y$

$\tt\implies \: x = 74 - 22$

$\tt\implies \: x = 52 \: years$

Hence ,

• Father's age is 52 years.

• Sons age is 22 years.