Question

10 years ago, a mans age was 6 times the age of his son .12 years later, the age of the sin will be 27 years .what is the present age of the father [brainliest for the best and detailed explantion]

Answer 1

Answer :

The present age of father is 40 years

while that of son is 15 years

Given :

• 10 years ago , a man's age was 6 times the age of his son
• 12 years later , the age of the son will be 27 years

To Find :

• The present age of the father

Solution :

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

According to question

$\sf \implies x - 10 = 6(y - 10) \\\\ \sf \implies x - 10 = 6y - 60 \\\\ \sf \implies x = 6y - 50........(1)$

Again by question

$\sf \implies y + 12 = 27 \\\\ \sf \implies y = 27 - 12 \\\\ \sf \implies y = 15$

Thus , the age of son is 15 years

Putting the value of x in (1)

$\sf \implies x = 6\times 15 - 50 \\\\ \sf \implies x = 90 - 50 \\\\ \sf \implies x = 40$

Therefore , the age of father is 40 years

Answer 2

GiveN :-

10 years ago, a mans age was 6 times the age of his son. 12 years later, the age of the son will be 27 years.

TO FinD :-

The present age of the father.

AcknowledgemenT :-

Let the age of the father be x years and the age of the son be y years.

SolutioN :-

CASE - I (10 years ago)

A/q,

$\tt{x-10 = 6(y-10)}\\\\\tt{\implies x-10=6y-60}\\\\\tt{\implies x-6y=-50}\:\:\:\: \dots(1)$

$\rule{150}{2}$

CASE - II (12 years later)

A/q,

$\tt{y+12=27}\\\\\tt{\implies y=27-12}\\\\\boxed{\tt{\implies y=15\ years}}$

$\rule{150}{2}$

Putting the value of y in eq.(1) :-

$\tt{x-6(15)=-50}\\\\\tt{\implies x=-50+90}\\\\\boxed{\underline{\tt{\implies x=40\ years}}} \:\:\:\:\:\:\:\: \dots \mathbf{ANSWER}$

Hence, the age of the father is 40 years.