Question

five years ago Nuri was thrice as old as Sonu ;10 years later Nuri will be twice as old as Sonu. How old are Nuri and Sonu? *

age of Nuri = 20 ;age of Sonu = 30

age of Nuri = 50 ; age of Sonu = 20

age of Nuri = 30 ; age of S​

Answer 1

Given Information :

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

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

To calculate :

• Present ages of Nuri and Sonu.

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Calculation :

Assumption: Let us assume the present ages of Nuri as x and present age of Sonu as y.

⠀⠀⠀⠀

${\underline{ \sf{ \pmb{ \bigstar \: According \: to \: the \: Question :}}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\dashrightarrow \sf (x - 5) = 3(y - 5) \\ \\ \\ \dashrightarrow \sf x - 3y = - 10 \: \: \: . \: . \: . \: . \: . \: \pmb( \pmb{ \frak{Equation \: 1} \pmb)} \\ \\ \\ \dashrightarrow \sf (x + 10y) = 2(y + 10) \\ \\ \\ \dashrightarrow \sf x - 2y = 10 \: \: \: . \: . \: . \: . \: . \: \pmb( \pmb{ \frak{Equation \: 2} \pmb)}$

⠀⠀⠀⠀⠀⠀

$\dag \: \underline{\bf{Now, subtracting \: Eq. 1 \: from \: Eq. 2}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\dashrightarrow \sf (x - 2y) - (x - 3y) = 10 + 10 \\ \\ \\ \dashrightarrow\sf -2y + 3y = 20 \\ \\ \\ \dashrightarrow\underline{ \boxed{\sf{ \pmb{ \pink{y = 20}}}}} \rm_{(Sonu's \: present \: age)}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\dag \: \underline{\bf{Now, substituting \: value \: of \: y \: in \: Eq. 2}}$

⠀⠀

$\dashrightarrow \sf 2 \times 20 + 10 \\ \\ \\ \dashrightarrow \sf \: \underline{ \boxed{ \sf{ \pmb{ \red{x = 50}}}}}\rm_{(Nuri's \: present \: age)}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Therefore, the present age of Nuri is 50 years and Sonu is 20 years old.

Answer 2

⠀Question:

Five years ago Nuri was thrice as old as Sonu ;10 years later Nuri will be twice as old as Sonu. How old are Nuri and Sonu?

Given that:

• Five years ago Nuri was thrice as old as Sonu

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

To Find:

• The measure of the age of Nuri

• The measure of the age of Sonu

Solution:

— Here we have been said that the age of Nuri 5 years ago was 3 times the age of Sonu and after 10 years Nuri will be twice old as Sonu , So let's consider the age of Nuri as x and the age of Sonu as y,

According to the question:

→ Nuri's age 5 years ago will be ( x - 5 ) years

→ Sonu's age 5 years ago will be ( y - 5 ) years

★ As per 1st statement,

$\longrightarrow \tt ( x - 5 ) = 3 ( y - 5 )$

$\longrightarrow \tt x - 5 = 3y - 15$

$\longrightarrow \tt x - 3y = - 10 --- ( 1 )$

→ Nuri's age after 10 years will be ( x + 10 ) years

→ Sonu's age after 10 years will be ( y + 10 ) years

★ As per 2nd statement,

$\longrightarrow \tt ( x + 10 ) = 2(y + 10 )$

$\longrightarrow \tt x - 10 = 2y + 20$

$\longrightarrow \tt x - 2y = 10 ---(2)$

Now let's subtract equation 1 from the second one elimination the variable x from them and find the value of y

$\longrightarrow \tt ( x - 2y ) - ( x - 3y) = 10 + 10$

$\longrightarrow \tt \cancel{x} - 2y \;\cancel{- x } + 3y = 20$

$\longrightarrow \tt - 2y + 3y = 20$

$\longrightarrow \tt y = 20$

• Henceforth the age of Sonu is 20 years

Now let's substitute the value of y = 20 in the 2nd equation and find the age of Nuri

$\longrightarrow \tt x - 2y = 10$

$\longrightarrow \tt x - 2(20) = 10$

$\longrightarrow \tt x - 40 = 10$

$\longrightarrow \tt x = 10 + 40$

$\longrightarrow \tt x = 50$

• Henceforth the age of Nuri is 50 years

Therefore:

• The age of Nuri and Sonu are 50 years and 20 years respectively