Question

Five years ago Nuri was thrice as old as Sun 10 year letter no he will be twice as old as Sun how old are Nuri and Sonu

Answer 1

$\large{\underline{\bf{\red{Correct\:Question:-}}}}$

Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu.

$\large{\underline{\bf{\blue{Given:-}}}}$

• ✦ Five years ago Nuri was thrice as old as Sonu.
• ✦ 10 years later Nuri will be twice as old as Sonu.

$\large{\underline{\bf{\blue{To\:Find:-}}}}$

• ➝ present age of Nuri and Sonu.

$\huge{\underline{\bf{\green{Solution:-}}}}$

Let the present age of Nuri be x years.

and, Let the present age of Sonu be y years.

Five years ago Nuri was thrice as old as Sonu.

➝ Age of Nuri = (x -5) year's

➝ Age of Sonu = (y -5) year's

According to 1st condition:-

➝ ( x -5 )= 3(y -5)

➝ (x -5) = 3y -15

➝ x - 3y = -10 .............(i)

Now,

10 years later Nuri will be twice as old as Sonu.

Age of Nuri = x+10 years

Age of Sonu = y +10 years

According to 2nd condition:-

➝ (x+10) = 2(y+10)

➝ x+10 = 2y + 20

➝ x - 2y = 10 .............(ii)

From equation (i) and (ii) , we get,

x - 3y = -10

x- 2y = 10

-- ⠀+⠀⠀--

⠀⠀-y = -20

we get, y = 20

putting value of y in equation (i)

➝ x - 3y = -10

➝ x -3×20 = -10

➝ x - 60 = -10

➝ x = 50

Hence,

Age of Nuri is x = 50 year's

Age of Sonu y = 20 year's.

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Answer 2

$\bold\blue{Correct \ Question}$

Five years ago Nuri was thrice as old as Sonu, 10 years later he will be twice as old as Sonu, how old are Nuri and Sonu?

$\huge\purple{\underline{\underline{\pink{Ans}\red{wer:}}}}$

$\sf{Present \ ages \ of \ Nuri \ and \ Sonu \ are}$

$\sf{50 \ and \ 20 \ years \ respectively.}$

$\sf\orange{Given:}$

$\sf{\implies{Five \ years \ ago \ Nuri \ was \ thrice}}$

$\sf{as \ old \ as \ Sonu.}$

$\sf{\implies{10 \ years \ later, \ Nuri \ will \ be}}$

$\sf{twice \ old \ as \ Sonu.}$

$\sf\pink{To \ find:}$

$\sf{Their \ present \ ages.}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{Let \ the \ Nuri's \ age \ be \ x \ years \ and}$

$\sf{Sonu's \ age \ be \ y \ years. }$

$\sf{According \ to \ first \ condition.}$

$\sf{\implies{x-5=3(y-5)}}$

$\sf{\implies{x-5=3y-15}}$

$\sf{\implies{x-3y=-10...(1)}}$

$\sf{According \ to \ second \ condition.}$

$\sf{\implies{x+10=2(y+10)}}$

$\sf{\implies{x+10=2y+20}}$

$\sf{\implies{x-2y=10...(2)}}$

$\sf{Subtract \ eq(1) \ from \ eq(2)}$

$\sf{x-2y=10}$

$\sf{-}$

$\sf{x-3y=-10}$

_________________

$\sf{\imples{y=20}}$

$\sf{Substitute \ y=20 \ in \ eq(1)}$

$\sf{\implies{x-3(20)=-10}}$

$\sf{\implies{x-60=-10}}$

$\sf{\implies{x=-10+60}}$

$\sf{\implies{x=50}}$

$\sf\purple{\tt{\therefore{Present \ ages \ of \ Nuri \ and \ Sonu \ are}}}$

$\sf\purple{\tt{50 \ and \ 20 \ years \ respectively.}}$