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?

Answer 1

Answer:

Let the present age of Nuri be X, and

Let the present age of Sonu be Y.

Five years ago :-

=> (x-5) =3(y-5)

=> X-5 = 3y - 15

=> X-3y = - 10 .......... (1)

Ten years later :-

=> (x+10) = 2(x+10)

=> x+10 = 2x + 20

=> x-2y = 10. ........... (2)

Subtratct euation 2 from 1

=> X - 3y - x + 2y = -10 - 10

=> -y = - 20

=> y = 20

Put the value of y in equation 1:-

=> x - 60 = - 10

=> x = 50

So, Nuri's prsent age is 50 years and Sonu's present age is 20 years.

Answer 2

$\boxed{\bf \: Question : - }$

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?

$\red{ \bullet } \: \bf \: Note : - \: This \: problem \: is \: solved \: by \: \red{elimination \: method}.$

$\boxed{ \bf \: Solution : - }$

$\rm{ \: Let \: the \: present \: age \: of \: Nuri \: be }\: \red{x} \: year \: and \: \\ \rm \: the \: present \: age \: of \: Sonu \: be \: \red{y} \: year.$

$\rm \: 5 \: year \: ago, \: Nuri's \: age \: = (x - 5) \: year$

$\rm \: and \: \: \ \: \: \: \: \: \: \: Sonu's \: age \: = (y - 5) \: year$

$\rm \: According \: to \: the \: question ,\: x - 5 = 3(y - 5)$

$\implies \: \: \: \: \: \: \: \: \: \: \: \: \: \rm \: x - 3y = - 10 \: \: \: \: ...(i)$

$\rm \: After \: 10 \: year, \: Nuri's \: age = (x + 10) \: year$

$\rm \: and \: Sonu's \: age \: = (y + 10) \: year$

$\rm \: According \: to \: the \: question,$

$\rm \: \: \: \: \: \: \: \: \: \: \: \: x + 10 = 2(y + 10) \implies \: x - 2y = 10 \: \: \: \: ...(ii)$

$\rm \: On \: subtracting \: Eq. \: (i) \: from \: Eq. \: (ii), \: we \: get$

$\rm \: (x - 2y) - (x - 3y) = 10 + 10 \implies \: - 2y + 3y = 20 = 20$

$\rm \: On \: subtracting \: y = 20 \: in \: eq. \: (ii), \: we \: get$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \rm \: x - 2 \times 20 = 10 \implies \: x = 50$

$\rm \: Therefore, \: present \: age \: of \: Nuri \: is \: \red{50} \: year \\ \rm \: and \: present \: age \: of \: Sonu \: is \: \red{20} \: year.$

$\boxed{ \bf \: \purple{ Hope \: it's \: helps \: you :) }}$