Question

The age of the father is 3 years more than three times the age of the son.Three years hence,fathers age will exceed twice the age of the son by 13 years.What will be their ages after 4 years.

Answer 1

Given that:

• The age of the father is 3 years more than three times the age of the son.
• Three years hence, father's age will exceed twice the age of the son by 13 years.

To Find:

• What will be their ages after 4 years.

Let us assume:

• The age of the son be x.
• Father's age = 3x + 3

Three years hence:

• Son's age = x + 3
• Father's age = 3x + 3 + 3

According to the question:

Father's age = 2(Son's age) + 13

↠ 3x + 3 + 3 = 2(x + 3) + 13

↠ 3x + 6 = 2x + 6 + 13

↠ 3x - 2x = 6 + 13 - 6

↠ x = 13

Their present ages:

• Son's age = x = 13 years
• Father's age = 3x + 3 = 3(13) + 3 = 42 years

Ages after 4 years:

• Son's age = 13 + 4 = 17 years
• Father's age = 42 + 4 = 46 years

Hence,

• After 4 years, the age of son will be 17 years and father's age will be 46 years.

Answer 2

Let,

• The age of son = s

• The age of father = 3s + 3

After three years,

• The age of son = s + 3

• The age of father = 3s + 3 + 3

From the question,

$\sf\to \: \: {3s + 3 + 3 = 2(s + 3) + 13}$

$\sf\to \: \: {3s + 6 = 2(5 + 3) + 13}$

$\sf\to \: \: {3s + 6 = 2s + 6 + 13}$

$\sf\to \: \: {3s + 6 = 2s + 19}$

$\sf\to \: \: {3s + 6 - 2s = 19}$

$\sf\to \: \: {s + 6 = 19}$

$\sf\to \: \: {s = 19 - 6}$

$\sf\large {\frak\orange{\rightsquigarrow \: \: { s = 13}}}$

Verification

Substituting s = 13 on the LHS,we get

3(13)+3+3

= 39+6

= 45

Substituting s = 13 on the RHS,we get

2(13+3)+13

= 26+6 +13

= 32+13

= 45

45 = 45

LHS = RHS

Hence, verified!!

Therefore,

• Present age of son = s = 13yrs

• Present age of father = 3s+3 = 3×13+3

= 39 + 3 = 42yrs

Ages after 4 yrs,

Son's age = 13 + 4 = 17yrs

Father's age = 42 + 4 = 46yrs

Henceforth, ages of son and his father after four years are 17yrs and 46yrs respectively.