Question

the sum of ages of father ans his son is 60 years. after 14 years,fathers age will be three times the age of the son. find their present ages​

Answer 1

$\bf{\huge{\underline{\boxed{\sf{\red{Answer:}}}}}}$

$\bf{\underline{\underline{\sf{\green{Given:}}}}}$

• The sum of ages of father ans his son is 60 years
• After 14 years , Father's age will be three times the age of the Son

$\bf{\underline{\underline{\sf{\green{To\:find\::}}}}}$

• Present age of Father
• Present age of Son

$\bf{\underline{\underline{\sf{\green{Solution:}}}}}$

Let the present age of Father be x years.

Let the present age of Son be y years.

$\bf{\underline{\underline{\sf{\orange{As\:per\:first\:condition:}}}}}$

• The sum of ages of father ans his son is 60 years

Representing the given condition mathematically.

=> Father's age + Son's age = 60

=> x + y = 60 ----> 1

$\bf{\underline{\underline{\sf{\orange{As\:per\:second\:condition:}}}}}$

• After 14 years , Father's age will be three times the age of the Son.

Ages after 14 years :-

Father's age = x + 14 years

Son's age = y + 14 years

Representing the condition mathematically.

=> x + 14 = 3 ( y + 14)

=> x + 14 = 3y + 42

=> x - 3y = 42 - 14

=> x - 3y = 28 ----> 2

Solve equations 2 and 1 simultaneously by elimination method.

Subtract equation 2 from equation 1,

....+ x + y = 60 ----> 1

- ( + x - 3y = 28 ) -----> 2

________________

4y = 32

y = $\sf\frac{32}{4}$

y = 8

Substitute the value of y in equation 2,

=> x - 3y = 28

=> x - 3 ( 8 ) = 28

=> x - 24 = 28

=> x = 28 + 24

=> x = 52

$\bf{\large{\underline{\boxed{\sf{\purple{Present\:age\:of\:father\:=\:x\:=\:52\:years}}}}}}$

$\bf{\large{\underline{\boxed{\sf{\purple{Present\:age\:of\:son\:=\:y\:=\:8\:years}}}}}}$

$\bf{\huge{\underline{\boxed{\sf{\red{Verification:}}}}}}$

For first case :-

• The sum of ages of father ans his son is 60 years

Present age of Father = x = 52 years

Present age of Son = y = 8 Years

=> Father's age + Son's age = 60

=> x + y = 60

=> 52 + 8 = 60

=> 60 = 60

LHS = RHS.

For second case :-

• After 14 years , Father's age will be three times the age of the Son

Ages after 14 years :-

Father = x + 14 = 52 + 14 = 66 years

Son = y + 14 = 8 + 14 = 22 years

=> x + 14 = 3 ( y + 14)

=> 66 = 3 ( 22)

=> 66 = 66

LHS = RHS.

Hence verified.

Answer 2

This question can be solved by both Linear equation in one variable as well as Linear equation in two variables.

I am solving with Linear equation at first.

According to question,

1. Sum of Son's and Father's age is 60.

2. After 14 years, father's age will be 3 times of Son's age.

Let the age of Son = x

And Father's age = 60-x

After 14 years,

Son's age = X+14

Father's age = 74-x

3(X+14) = 74-x

3x + 42 = 74-x

4x = 32

x = 8 years.

Hence,

Son's age = X = 8 years

Father's age = 60-x = 52 years.

Now, solving by Linear equation in two variables.

Son's age = x years

Father's age = y years

x + y = 60 -------(1)

Now, After 14 years,

3(x+14) = y+14

3x - y = 42-14

3x-y = 28 ------(2)

From (1) & (2)

x+y = 60

3x-y = 28

______________

4x = 32

x = 32/4

x = 8 years.

Putting the value of x in eq (1)

x + y = 60

8 + y = 60

y = 52 years.

x = 8 years. Answer....