Question

Six years hence a man’s age will be three times his son’s age, and three years ago he was nine times as old as his son at that time. Find their present ages.

Answer 1

answer: Let the age of man be x

and the age of his son be y

According to the question:

After 6 years :  

(x+6)=3(y+6)

⇒x−3y=12⟶(i)

Three years ago :

x−3=9(y−3)

⇒x−3=9y−27

⇒x−9y=−24⟶(ii)

Solving (i) and (ii),  

6y=36

⇒y=6

Putting value of y in equation (i),

x−3xy=12

∴x=12+18

x=30

∴ Age of man =30 years.

  Age of son =6 years.

Answer 2

Answer:

✒ Question:

$\textsf{Six years hence a man 's age will be three times}$$\textsf{his son 's age , and three years ago he was nine}$$\textsf{times as old as his son at that time . Find their}$$\textsf{present age.}$

✒ To find:

$\textsf{(i) The age of the man}$

$\textsf{(ii) The age of his son}$

✒ Taken:

Let the age man be x

And

Let the age of the son be y

A/Q:

• After 6 years : (Equation 1)

Taken the equation as

(x+6)=3(y+6)

• Then , after 3 years ago : (Equation 2)

Taken the equation as

x-3=9(y-3)

• After that solve the equation 1 and 2

• At last find the age of both man and his son.

✒ Concept:

▪︎First find the answer of the equation 1.

▪︎Then find the answer of the equation 2.

▪︎Then solve both equation at a time.

▪︎The age of the son will come.

▪︎Then find the age of the man.

✒ Solution:

After 6 years:

$\bold\purple{Taken,(x+6)=3(y+6)}$

=> x+6=3y+18

=> x-3y=18-6

=> x-3y=12

__________________________________

After 3 years:

$\bold\purple{Taken,x-3=9(y-3)}$

=> x-3=9y-27

=> x-9y=-27+3

=> x-9y=-24

__________________________________

Solving equation 1 and equation 2:

=> -3y-(-9y)=12-(-24)

=> -3y+9y=12+24

=> 6y=36

=> y=36/6

=> y=6

__________________________________

Now , age of the man by taking y at equation 1:

=> x-3xy=12

=> x-3(6)=12

=> x-18=12

=> x=12+18

=> x=30

✒ Answer:

Age of the man = 30 years

Age of his son = 6 years

✒ Extra information:

In the answer :

Cross multiplication is used :

For example :

= 3(4)

= So , there will be 3 × 4

= 12

HOPE IT HELPS YOU