Question

Five years ago , father was thrice as old as son. Ten years later , father will be twice as old as son. Find the age of father and son​

Answer 1

Answer:

Let the son's age be x

Then the father's age will be 3x.

After 12 yrs.

Son's age = x+12

Father's age = 3x+12

Now according to the condition,

Father's age after 12 yrs. wil be = 2(x+12) = 2x+24

∴ 3x+12 = 2x+24

x = 12

∴ The son's age = 12

& the father's age = 3×12=36

Answer 2

$\huge\bold{\gray{\sf{Answer:}}}$

Explanation:

Given :

Five years ago , father was thrice as old as son. Ten years later , father will be twice as old as son.

To Find :

Age of father and son.

ㅤㅤㅤㅤㅤㅤㅤ

Let the father's age be 'x'

Let the father's age be 'x'And son's age be 'y'

5 years ago the age of father was x-5

and son's age was=y-5

Question said 5 years ago father was thrice as old as son

$x - 5 = 3(y - 5)$

$= > x - 5 = 3y - 15$

$\bold{= > x - 3y = - 10......(1)}$

Now ,after 10 Years father age will be x+10

Son's age will be y+10

Question said after 10 years father will be twice as old as son :

$= > x + 10 = 2(y + 10)$

$= > x + 10 = 2y + 20$

$\bold{= > x - 2y = 10.......(2)}$

Solving equation (1) and equation (2)by eliminating method:

ㅤㅤㅤㅤㅤx-2y=10

ㅤㅤㅤㅤ x-3y=-10

ㅤㅤㅤㅤ(-)ㅤ(+)ㅤ(+)

ㅤㅤㅤㅤ_________

ㅤㅤㅤㅤㅤ3y-2y=10+10

ㅤㅤㅤㅤㅤㅤy=20

∴Son's age is $\bold{\green{20 \:Years}}$

=>x-2y=10

=>x-2×20=10

=>x-40=10

=>x=10+40

=>x=50

Father's age is $\bold{\green{50\: years }}$

Check :-

5 Years ago father was thrice as old as son

$x - 5 = 3(y - 5)$

$5 0- 5 = 3(20 - 5)$

$45 = 45$