Question

1) Father in aged three times more than his son Ronit.
After 8 years he would be two
and a half times of Ronit's age. After further 8 years, how many times would he be of Ronit's age ?
​

Answer 1

Given,

• Father age is three times more than his son Ronit.
• After 8 years he would be two and a half times of Ronit's age .

To Find,

• After 8 years How many times would he be of Ronit's Age.

Solution :

$\implies$ Suppose the Ronit and his father Age be a years.

Therefore,

$\mapsto \underline{\sf{\pink{According \ to \ the \ First \ Condition :}}}$

• Father age is three times more than his son Ronit.

$\implies \sf{The \ Ronit \ Age = a \ years }$

$\implies \sf{Ronit's \ Father \ Age = 3a \ years}$

$\mapsto \underline{\sf{\pink{According \ to \ the \ Second \ Condition :}}}$

• After 8 years he would be two and a half times of Ronit's age .

Therefore,

• After 8 years Ronit age = a + 8
• After 8 years Ronit's Father age = 3a + 8

$\implies \sf{3a + 8 = 2.5(a + 8)}$

$\implies \sf{3a + 8 = 2.5a + 20}$

$\implies \sf{3a - 2.5a = 20 - 8}$

$\implies \sf{0.5a = 12}$

$\implies \sf{a = \dfrac{12}{0.5}}$

$\implies \sf{a = \dfrac{120}{5}}$

$\implies \boxed{\sf{a = 24 \ years}}$

Therefore,

• Ronit age = 24 years
• Ronit's Father age = 3 x 24 = 72 years

After Furture 8 years :

$\boxed{\large{\sf{\red{After\:Further\:8\:years\:Ronit\:Age = 24 + 8 = 32 \ years}}}}$

$\boxed{\large{\sf{\red{After\:Further\:8\:years\:Ronit's\:Father\:Age = 72 + 8 = 80 \ years}}}}$

Therefore,

$\implies$ After Further 8 years The Age of Father will be 2.2 times of Ronit's age.

$\rule{200}2$

Answer 2

Gɪᴠᴇɴ

Father's age is three times Rohit's age.

After 8 years, father's age will be 2 & ½ times Rohit's age.

Tᴏ ꜰɪɴᴅ

After further 8 years, how many times of Rohit's age is father's age.

Sᴏʟᴜᴛɪᴏɴ

Let present age of Rohit be n years & present age of father be 3n years.

Case ➊ 

⇒ (3n + 8) = (n + 8) × (5/2)

⇒ 3n + 8 = 5(n + 8)/2

⇒ 3n + 8 = (5n + 40)/2

⇒ 2(3n + 8) = 5n + 40

⇒ 6n + 16 = 5n + 40

⇒ 6n - 5n = 40 - 16

⇒ n = 24

Now finding present ages :

⇾ Age of Rohit = n = 24 years.

⇾ Age of father = 3n = 3(24) = 72 years.

Now finding ages after further 8 years :

Here, after further 8 years age of them will be (n + 8 + 8) = (n + 16) & (3n + 8 + 8) = (3n + 16) years respectively.

⇾ Age of Rohit will be = 24 + 16 = 40 years.

⇾ Age of father will be = 72 + 16 = 88 years.

Now finding the answer :

⇾ Age of father is (88/40) times of Rohit's age.

⇾ Age of father will be 2.2 times of Rohit's age.

Tʜᴇʀᴇꜰᴏʀᴇ,

Age of father will be 2.2 times or (2 & 1/5) times of Rohit's age after further 8 years.