Question

A father and his son decides to sum their ages. The sum is equal to sixty years.six years ago the age of the father was five times the age of the son. six years from now the son's age will be?​

Answer 1

Answer:

Son will be 20 years old, 6 years from now.

Step-by-step explanation:

We can solve it in two ways

Method 1 (Single variable)

Let son's present age be x,

then father's age will be (60 - x).

We know that,

They add upto 60,

So,

x + (60 - x) = 60

x + 60 - x = 60

60 = 60

Hence, it is correct.

Then,

6 years ago,

Father's age = 60 - x - 6 = (54 - x)

Son's age = (x - 6)

Now,

According to the Question,

Father's age = 5 × Son's age (6 years ago)

54 - x = 5(x - 6)

54 - x = 5x - 30

5x + x = 54 + 30

6x = 84

x = 84/6

x = 14

Hence,

Son's present age is 14 years.

But we need his age 6 years from now,

Then,

Son's age = 14 + 6 = 20

Hence,

Son will be 20 years old, 6 years from now.

Method 2 (Linear equation in 2 variables)

Let father's present age be x and son's present age be y.

Then,

According to the Question,

x + y = 60

x = 60 - y ----- 1

Also,

Six years ago,

Father's age = (x - 6)

Son's age = (y - 6)

Then, according to the Question,

(x - 6) = 5(y - 6)

x - 6 = 5y - 30

x - 5y = 6 - 30

x - 5y = -24

From eq.1,

(60 - y) - 5y = -24

60 - y - 5y = -24

60 - 6y = -24

6(10 - y) = -24

10 - y = -24/6

10 - y = -4

y = 10 + 4

y = 14 years

Hence,

Son's present age is 14 years.

But we need his age 6 years from now,

Then,

Son's age = 14 + 6 = 20

Hence,

Son will be 20 years old, 6 years from now.

Hope it helped and believing you understood it........All the best