Question

Jack's present age is one fourth of his father's age two years ago.
Jack's father's age will be twice Raman's age after 10 years. If
Raman's 12th birthday was celebrated 2 years ago, then what is
Jack's present age?​

Answer 1

Required Answer:-

Let's choose the third statement i.e. Raman's 12th birthday was celebrated 2 years ago and interpret first.

• Raman was 12 years old 2 years ago.
• Then he is 12 + 2 = 14 years old now.

Jack's father's age will be twice Raman's age after 10 years.

• After 10 years, Raman's age = 14 + 10 = 24
• Jack's father will be 24 × 2 = 48 yrs after 10 years.
• Then Jack's father's age now = 48 years - 10 years = 38 years.

Jack's present age is one fourth of his father's age two years ago.

• Jack's father age 2 years ago = 38 years - 2 years = 36 years.
• Jack's present age according to statement, 1/4 × 36 years = 9 years$.$

Hence:-

The current or the present age of Jack is $\boxed{\purple{\Huge{\sf{9\: years}}}}$

Answer 2

${\large{\underline{\pmb{\frak{Given...}}}}}$

★ Jack's present age is one fourth of his father's age two years ago.

★ Jack's father's age will be twice Raman's age after 10 years

★ Raman's 12th birthday was celebrated 2 years ago.

${\large{\underline{\pmb{\frak{To\; Find...}}}}}$

★ what is  Jack's present age?

${\large{\underline{\pmb{\frak{Let's \; understand \; the \; concept...}}}}}$

❍ Concept : Here, we have been said that the present age of Jack is 1/4 of his father's age 2 years ago, Jack,s father's age will be twice the age of Raman after 10 years and that Raman,s 12th birthday was celebrated 2 years back.

★ Now, as we've been provided with the clues about their ages let's use these statements and frame expression, equations and find their solutions to find their ages accordingly.

${\large{\underline{\pmb{\frak{Solution...}}}}}$

★ The present age of Jack is 9 years

${\large{\underline{\pmb{\frak{Full\; solution...}}}}}$

~ Now as we have been said the 12th birthday of Raman was celebrated 2 years back. let's find his present age adding 2 years to 12 so, that we'll have the base age to find the ages of the others,

${\bigstar{\underline{\sf{According\; to \; the \; question...}}}}$

$\implies \sf Raman's \; age \; two\; years \; back = 12$

$\implies \sf Raman's \; present \; age = 12 + 2 = 14 years$

• Henceforth Raman's present age is 14 years

${\bigstar{\underline{\sf{As\; we\; know \; that...}}}}$

⋆ Jack's father's age will be twice the age of raman after 10 years.

~ So,  let's find  the age of Jack's father on the basis of raman's age

$\implies \sf Raman's \;age \; after\; 10 \;years = 14 + 10$

$\implies \sf Raman's \;age \; after\; 10 \;years = 24 \; years$

$\implies \sf Jack's\;father's\; age\; after \; 10 \; years = 24 \times 2$

$\implies \sf Jack's\;father's\; age\; after \; 10 \; years = 48\; years$

$\implies \sf Jack's\;father's\; age\; at \; present = 38\; years$

• Henceforth the age of Jack's father is  38

${\bigstar{\underline{\sf{As\; per \; statement\; 1..}}}}$

⋆ Jack's present age is one fourth of his father's age two years ago.

~ Now let's find the age of Jack's father 2 years back and then find the 1/4 th of it to find Jack's age.

${\implies} \sf Jack's\;father's\; age\; before \; 2\; years = 38-2 years$

${\implies} \sf Jack's\;father's\; age\; before \; 2\; years = 36 \; years$

${\bigstar{\underline{\purple{\underline{\sf{Thereby...}}}}}}$

$\implies \sf Jack's\; present\; age\; = 1/4 \times 36$

$\implies \sf Jack's\; present\; age\; = 9 years$

• Therefore the present age of Jack is 9 years