Question

. A father is 30 years older than his son however he will be only thrice as old as the son after 5 years
what is father s present age ?
(a) 40 yrs
(b) 30 yrs
(c) 50 yrs
(d) None of these

Answer 1

Answer:

Option a) 40 years

Father is 40 year old and son is 10 year old.

Step-by-step explanation:

Father is = 30 years older than son

After 5 years, father will be thrice the age of his father.

Let the present ages be -

• Son as y
• Father as (y + 30)

Ages after 5 years -

• Son = (y + 5)
• Father = (y + 30) + 5

According to the Question,

$\longrightarrow$ 3(y + 5) = y + 30 + 5

$\longrightarrow$ 3y + 15 = y + 35

$\longrightarrow$ 3y - y = 35 - 15

$\longrightarrow$ 2y = 20

$\longrightarrow$ y = 10

Son's present age = 10 years

______________________________

★ Father's present age =

$\longrightarrow$ (10 + 30)

$\longrightarrow$ 40 years

Therefore, father is 40 year old and son is 10 year old.

Answer 2

Answer:

Given :-

• A father is 30 years older than his son.
• However he will be only thrice as old as the son after 5 years.

To Find :-

• What is the present age of father.

Solution :-

Let,

$\mapsto \sf\bold{Present\: age\: of\: son =\: x\: years}$

$\mapsto \sf\bold{Present\: age\: of\: father =\: (x + 30)\: years}$

After 5 years :

$\mapsto$ Age of son :

$\leadsto \sf \bold{\green{(x\: + 5)\: years}}$

$\mapsto$ Age of father :

$\leadsto \sf (x + 30 + 5)\: years$

$\leadsto \sf\bold{\green{(x + 35)\: years}}$

According to the question,

$\implies \sf 3(x + 5) =\: (x + 35)$

$\implies \sf 3x + 15 =\: x + 35$

$\implies \sf 3x - x =\: 35 - 15$

$\implies \sf 2x =\: 20$

$\implies \sf x =\: \dfrac{\cancel{20}}{\cancel{2}}$

$\implies \sf x =\: \dfrac{10}{1}$

$\implies \sf\bold{\purple{x =\: 10\: years}}$

Hence, the required present age of son and his father are :

$\mapsto$ Present age of son :

$\longrightarrow \sf x\: years$

$\longrightarrow \sf\bold{\red{10\: years}}$

$\mapsto$ Present age of father :

$\longrightarrow \sf (x + 30)\: years$

$\longrightarrow \sf (10 + 30)\: years$

$\longrightarrow \sf\bold{\red{40\: years}}$

Hence,

$\bigstar\: \: \sf\bold{Present\: age\: of\: son =\: 10\: years}$

$\bigstar\: \: \sf\bold{Present\: age\: of\: father =\: 40\: years}$

$\therefore$ The present age of father is 40 years.

Hence, the correct options is option no (a) 40 years.

VERIFICATION :-

$\implies \sf 3(x + 5) =\: (x + 35)$

$\implies \sf 3x + 15 =\: x + 35$

By putting x = 10 we get,

$\implies \sf 3(10) + 15 =\: 10 + 35$

$\implies \sf 30 + 15 =\: 45$

$\implies \sf\bold{45 =\: 45}$

Hence, Verified.