Question

5 years, ago Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as sonu. How old are they ? pls ans fast

Answer 1

$\large\bf\underline \blue {To \: \mathscr{f}ind:-}$

• ♪ we need to find the present age of nuri and sonu

$\huge\bf\underline \red{ \mathcal{S}olution:-}$

$\bf\underline{\purple{Given:-}}$

• 5 years, ago Nuri was thrice as old as Sonu.
• Ten years later, Nuri will be twice as sonu

${ \blue{ \mathscr{ \underline{Let : - }}}}$

Let present age of sonu be x years.

Let the present age of Nuri be y years.

$\underline{ \large \purple{ \mathscr{\dag\:A \bf{ccourding} \: to \: \mathscr {Q} \bf{uestion} ....}}}$

5 years ago :-

• Age of Sonu = x - 5
• Age of Nuri = y - 5

5 years ,Ago Nuri was thrice as old as Sonu

⟶ y - 5 = 3(x - 5)

⟶ y - 5 = 3x - 15

⟶ y + 10 = 3x

⟶ 3x - y = 10 ....1)

Ten years later, Nuri will be twice as sonu

Ten years later :-

• Age if sonu = x + 10
• Age of Nuri = y + 10

⟶ y + 10 = 2(x + 10)

⟶ y + 10 = 2x + 20

⟶ y - 2x = 10 ....2)

• From equation ...1)

⟶ 3 x - y = 10

⟶ - y = 10 - 3x

⟶ y = 3x - 10 ....3)

• Substituting value of y in ...2)

⟶ y - 2x = 10

⟶ 3x - 10 - 2x = 10

⟶ x - 10 = 10

⟶ x = 10 + 10

⟶ x = 20

• Putting value of x in ....3)

⟶ y = 3x - 10

⟶ y = 3 × 20 - 10

⟶ y = 60 - 10

⟶ y = 50

Hence,

• Age of Sonu x = 20 years.
• Age of Nuri y = 50 years.

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Answer 2

$\huge\sf\red{\underline{\underline{Given}}}\::$

• $\sf\gray{5 \ years, \ ago \ Nuri \ was \ thrice \ as \ old \ as \ Sonu}$
• $\sf\gray{Ten \ years \ later, \ Nuri \ will \ be \ twice \ as \ Sonu.}$

$\huge\sf\green{\underline{\underline{To\:Find}}}\::$

• $\sf\gray{Present \ ages \ of \ Nuri \ and \ Sonu}$

$\huge\sf\pink{\underline{\underline{Solution}}}\::$

${\Large\mathfrak\red{Let}}\begin{cases}\sf\underline\orange{Age \ of \ Nuri \ = \ x \ years} \\\sf\underline\orange{Age \ of \ Sonu \ = \ y \ years}\end{cases}$

$\star\:\:\sf\underline\red{5 \ years \ ago} \ :$

$\longrightarrow \:\:\:\sf\purple{(x - 5) = 3(y - 5)}$

$\longrightarrow \:\:\:\sf\blue{x-5 = 3y - 15}$

$\longrightarrow \:\:\:\sf\purple{x = 3y - 10.........(1)}$

$\star\:\:\sf\underline\red{10 \ years \ later} \ :$

$\longrightarrow \:\:\:\sf\purple{(x+10) = 2(y+10)}$

$\longrightarrow \:\:\:\sf\blue{x+10 = 2y+20}$

$\longrightarrow \:\:\:\sf\purple{x-2y = 10..........(2)}$

$\sf\underline\green{Substitute \ eq ( 1 ) \ in \ eq ( 2 )}$

$\longrightarrow \:\:\:\sf\purple{(3y -10) - 2y = 10}$

$\longrightarrow \:\:\:\sf\underline\blue{y \ = \ 20}$

$\sf\underline\green{Now, \ Substitute \ y \ value \ in \ eq(1)}$

$\longrightarrow \:\:\:\sf\purple{x = 3y - 10}$

$\longrightarrow \:\:\:\sf\blue{x = 3 × 20 - 10}$

$\longrightarrow \:\:\:\sf\underline\purple{x \ = \ 50}$

$\bf\underline\pink{Hence,}$

$\begin{cases}\bf\underline\red{Age \ of \ Nuri \ = \ 50 \ years} \\ \bf\underline\orange{Age \ of \ Sonu \ = \ 20 \ years}\end{cases}$