Question

If father is 30 year old then his soon in 12 year the man will be three times as old as his son find the present age

Answer 1

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Given :-

• Father is 30 year old then his Son
• In 12 year the man will be three times as old as his Son

To find :-

• Present age of Father
• Present age of Son

Sóĺúťíóń :-

Let the present age of father be x years

Let the present age of Son be y years

As per the first condition :-

• Father is 30 year old then his Son

Father = Son + 30

Let's represent it mathematically to get our first equation,

x = y + 30

x - y = 30 ----> 1

As per the second condition :-

• In 12 year the man will be three times as old as his Son

Ages in 12 years,

Father (man) = x + 12 years

Son= y + 12 years

Man will be three times as old as his son.

Let's represent it mathematically to get our second equation.

x + 12 = 3 ( y + 12)

x + 12 = 3y + 36

x - 3y = 36 - 12

x - 3y = 24 ----> 2

Solve equations 1 and 2 simultaneously by elimination method.

Subtract equation 2 from 1,

....+ x - y = + 30

- (+ x - 3y = + 24 )

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2y = 6

y = $\bf\large\frac{6}{2}$

y = 3

•°• Present age of son = y = 3 years

Substitute y = 3 in equation 1

x - y = 30 ---->

x - 3 = 30

x = 30 + 3

x = 33

•°• Present age of fatger= x = 33 years.

$\bf{\huge{\underline{\boxed{\rm{\green{Verification:}}}}}}$

For first case :-

• Father is 30 year old then his son

Father's present age = 33 years = x

Son's present age = 3 years = y

x = y + 30

33 = 3 + 30

33 = 33

LHS = RHS.

For second case :-

• In 12 year the man will be three times as old as his Son

Ages of father and son in 12 years :

Father = x + 12 = 33 + 12 = 45 years

Son = y + 12 = 3 + 12 = 15 years

x + 12 = 3 ( y + 12)

45 = 3 ( 15 )

45 = 45

LHS = RHS

Hence verified.