Question

Divya's father's age is 3times of her age.After 12 years her father's age is 2 times of her age.Find their present ages?​

Answer 1

Question:

Divya's father's age is 3 times of her age. After 12 years her father's age is 2 times of her age. Find their present ages.

Answer:

Divya's present age is 12 years and Divya's father's present age is 36 years.

Solution:

It is given that,

Divya's father's age is 3 times of her age.

Thus;

Let the present age of Divya be x years

and the present age of her father's age be 3x years.

Also,

Divya's age after 12 years will be ;

(x + 12) years.

And ,

Divya's father's age after 12 years will be ; (3x + 12) years.

According to the question;

After 12 years Divya's father is two times of her age.

ie;

=> 3x + 12 = 2(x + 12)

=> 3x + 12 = 2x + 24

=> 3x - 2x = 24 - 12

=> x = 12

Thus,

Divya's present age

= x years

= 12 years

And,

Divya's father's present age

= 3x years

= 3•12 years

= 36 years

Hence,

The present ages of Divya and her father are 12 years and 36 years respectively.

Answer 2

$\bold{\underline{\underline{Answer:}}}$

Present age of Father = 36 years.

Present age of Divya = 12 years.

$\bold{\underline{\underline{Step\:by\:step\:explanation:}}}$

Given :

• Divya's father's age is 3 times of her age
• After 12 years her father's age is 2 times of her age.

To find :

• Present age of Father
• Present age of Divya

Solution :

I'm solving with elimination method, kindly refer to @ankita9523's answer for solution with substitution method. Choose the method convenient for you! :)

Let me start,

Let present age of Father be x years.

Let present age of Divya be y years.

$\bold{\underline{\underline{As\:per\:the\:first\:given\:condition:}}}$

• Divya's father's age is 3 times of her age

Constituting it mathematically,

$\bold{x=3y}$

$\bold{x-3y=0}$ ---> (1)

$\bold{\underline{\underline{As\:per\:the\:second\:given\:condition:}}}$

• After 12 years her father's age is 2 times of her age.

Ages after 12 years :

Father = x + 12 years

Divya = y + 12 years

Constituting it mathematically,

$\bold{x+12=2(y+12)}$

$\bold{x+12=2y+24}$

$\bold{x-2y=24-12}$

$\bold{x-2y=12}$ ---> (2)

Solve equation 1 and equation 2 simultaneously by elimination method.

Subtract equation 2 from equation 1,

x - 3y = 0 --->(1)

x - 2y = 12 --> (2)

---------------

- y = - 12

•°• y = 12

Substitute y = 12 in equation 1,

x - 3y = 0

x - 3(12) = 0

x - 36 = 0

x = 36

•°• Present age of Father, x = 36 years.

Present age of Divya, y = 12 years.