Question

Six years hence a mans age will be three times as his son three years ago he was nine times a old as his son find their present ages

Answer 1

Step-by-step explanation:

Let’s assume the present ages of the father as x years and that of his son’s age as y years.

From the question it’s given that,

After 6 years,

the man’s age will be (x + 6) years

and

son’s age will be (y + 6) years.

So, the equation formed is

x + 6 = 3(y + 6)

x + 6 = 3y + 18

x – 3y – 12 = 0…….

(i) Also again from the question it’s given as,

Before 3 years, the age of the man was (x – 3) years and the age of son’s was (y – 3) years .

Furthermore, the relation between their 3 years ago is given below

x – 3 = 9(y – 3)

x – 3 = 9y – 27

x – 9y + 24 = 0…….

(ii) Thus, by solving (i) and (ii), we get the required solution

Using cross-multiplication,

we get

⇒x = 30, y = 6

Hence, the present age of the man is 30 years and the present age of son is 6

Answer 2

Answer:

Father's Age = 30

Son's Age = 6

Step-by-step explanation:

Age of man =  x

Age of son  = y

After 6 years :

x+6=3(y+6)

x+6=3y+18

x-3y = 12 ----------------------(i)

3 Years Ago :

x-3 = 9(y-3)

x-3 = 9y-27

x-9y = -24---------------------(ii)

Subtract the two equations(i)-(ii):

  x-3y = 12

-  x-9y = -24

= 6y = 36

y = 6

Substitute y in any of the 2 equations to get value of x

x-18=12

x=30

Therefore ages are :

Father's Age = 30

Son's Age = 6

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