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?
[tex]{\large{\underline{\pmb{\frak{Let’s \; understand \; the \; concept…}}}}}[/tex]
❍ 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.
~ 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,
[tex]{\bigstar{\underline{\sf{According\; to \; the \; question…}}}}[/tex]
[tex]\implies \sf Raman’s \; age \; two\; years \; back = 12[/tex]
Required Answer:–
Let’s choose the third statement i.e. Raman’s 12th birthday was celebrated 2 years ago and interpret first.
Jack’s father’s age will be twice Raman’s age after 10 years.
Jack’s present age is one fourth of his father’s age two years ago.
Hence:–
The current or the present age of Jack is [tex]\boxed{\purple{\Huge{\sf{9\: years}}}}[/tex]
[tex]{\large{\underline{\pmb{\frak{Given…}}}}}[/tex]
★ 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.
[tex]{\large{\underline{\pmb{\frak{To\; Find…}}}}}[/tex]
★ what is Jack’s present age?
[tex]{\large{\underline{\pmb{\frak{Let’s \; understand \; the \; concept…}}}}}[/tex]
❍ 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.
[tex]{\large{\underline{\pmb{\frak{Solution…}}}}}[/tex]
★ The present age of Jack is 9 years
[tex]{\large{\underline{\pmb{\frak{Full\; solution…}}}}}[/tex]
~ 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,
[tex]{\bigstar{\underline{\sf{According\; to \; the \; question…}}}}[/tex]
[tex]\implies \sf Raman’s \; age \; two\; years \; back = 12[/tex]
[tex]\implies \sf Raman’s \; present \; age = 12 + 2 = 14 years[/tex]
[tex]{\bigstar{\underline{\sf{As\; we\; know \; that…}}}}[/tex]
⋆ 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
[tex]\implies \sf Raman’s \;age \; after\; 10 \;years = 14 + 10[/tex]
[tex]\implies \sf Raman’s \;age \; after\; 10 \;years = 24 \; years[/tex]
[tex]\implies \sf Jack’s\;father’s\; age\; after \; 10 \; years = 24 \times 2[/tex]
[tex]\implies \sf Jack’s\;father’s\; age\; after \; 10 \; years = 48\; years[/tex]
[tex]\implies \sf Jack’s\;father’s\; age\; at \; present = 38\; years[/tex]
[tex]{\bigstar{\underline{\sf{As\; per \; statement\; 1..}}}}[/tex]
⋆ 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.
[tex]{\implies} \sf Jack’s\;father’s\; age\; before \; 2\; years = 38-2 years[/tex]
[tex]{\implies} \sf Jack’s\;father’s\; age\; before \; 2\; years = 36 \; years[/tex]
[tex]{\bigstar{\underline{\purple{\underline{\sf{Thereby…}}}}}}[/tex]
[tex]\implies \sf Jack’s\; present\; age\; = 1/4 \times 36[/tex]
[tex]\implies \sf Jack’s\; present\; age\; = 9 years[/tex]