Question

$\large{\sf{\underline{\underline\pink{Question!!}}}}$
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

Step-by-step explanation:

Let the present age of Nuri be x years and present age of sonu be y years.

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According to given conditions,

5 years ago,

x-5= 3(y-5)

x - 3y = -10(Eqn 1)

10 year later,

x + 10 = 2(y + 10)

x - 2y = 10 .(Eqn 2)

On subtracting eqn 1 from 2,

(x-2y) - (x - 3y) = 10 + 10

-2y+3y=20

y = 20

On substituting y = 20 in eqn 2,

x = 2 x 20 + 10

x = 50

Hence present age of Nuri is 50 years and present age of Sonu is 20 years

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Answer 2

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

$\sf{Let \: the \: present \: age \: of \: Nuri = x \: yrs}$

$\sf{And, the \: present \: age \: of \: Sonu = y \: yrs}$

Five years ago,

$\sf{Age \: of \: Nuri = x-5 years}$

$\sf{Age \: of \: Sonu = y-5 years}$

Nuri was thrice as old as Sonu.

Then,

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

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

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

$\small\implies\sf{x-3y = -10}-----(i)$

Ten years later,

$\sf{Age \: of \: Nuri = x+10}$

$\sf{Age \: of \: Sonu = y+10}$

Nuri will be twice as old as Sonu.

Then,

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

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

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

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

Subtracting equ. (i) from (ii) we get,

$\small\implies\sf{y = 20}$

Plug this value in eq. (i) we get,

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

$\implies\sf{x-3×20 = -10}$

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

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

$\sf{ Hence, Age \: of \: Nuri = 50 \: years}$

$\sf{And \: Age \: of \: Sonu = 20 \: years}$