Question

(ii) At present the age of the father is 6 times the age of the son. If the age of the father after 6 years is the son Age is 3 times, but how old is the father now? (a) 15 years (b) 19 years (c) 24 years (d) 12 years.​

Answer 1

GIVEN:

• Present age of father is 6 times the age of the son.
• After 6 years, the age of the father becomes 3 times the age of the age of the son.

TO FIND:

• What is the present age of father ?

SOLUTION:

Let the present age of the father be 'x' years and the present age of son be 'y' years

CASE:- 1)

❐ Present age of father is 6 times the age of the son.

${\underline{\underline{\bf{According \: To \: Question:-}}}}$

➜ x = 6y...❶

CASE:- 2)

❐ After 6 years, the age of the father becomes 3 times the age of the age of the son.

• Father's age = (x + 6) years
• Son's age = (y + 6) years

${\underline{\underline{\bf{According \: To \: Question:-}}}}$

➜ (x + 6) = 3(y + 6)

➜ x + 6 = 3y + 18

➜ x –3y = 18 –6

➜ x –3y = 12...❷

On putting the value of 'x' from equation 1) in equation 2), we get

➜ 6y –3y = 12

➜ 3y = 12

➜ y = $\sf{\cancel\dfrac{12}{3}}$

❮ y = 4 ❯

Now, put the value of 'y' in equation 2)

➜ x = 6 $\times$ 4

❮ x = 24 ❯

❝ Hence, the father's age(x) is 24 years ❞

______________________

Answer 2

Given :-

• Present age of father is 6 times the age of the son.
• After 6 years the age of the father becomes 3 times the age of the age of the son.

To Find :-

• Present age of father

Solution :-

Let the present age of the father be 'x' years.

Let the present age of son be 'y' years.

❮ CASE :- 1 ❯

• Present age of father is 6 times the age of the son.

So,

$\to\tt x = 6y - - - - ❶$

❮ CASE :- 2 ❯

• After 6 years the age of the father becomes 3 times the age of the age of the son.

So,

• Father's age = (x + 6) years
• Son's age = (y + 6) years

A.T.Q :-

$\implies \tt (x + 6) = 3(y + 6)$

$\implies \tt x + 6 = 3y + 18$

$\implies \tt x –3y = 18 –6$

$\implies \tt x –3y = 12 - - - ❷$

Putting the value of 'x' from equation (1) in equation (2),

$\implies \tt 6y –3y = 12$

$\implies \tt 3y = 12$

$\implies \tt y = \tt{\cancel\dfrac{12}{3}}$

$\implies \tt y = 4$

Now, put the value of 'y' in equation (2)

$\implies \tt x = 6 \times 4$

$\implies \tt x = 24$

Hence, the father's age is 24 years.