Question

10. Five years ago, Nuri was thrice as old ae Sonu. Ten years later, Nuri will be twice as old as sonu.How old are Nuri and Sonu?
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Answer 1

Let the present age of Nuri  = x year

And present age of Sonu = y year

Five years ago

Age of Nuri = x – 5 years

Age of Sony = y – 5 years

Nuri was thrice as old as Sonu

X- 5  =  3(y – 5)

X – 5  =  35 – 15

X – 3y  =  -15  + 5

X – 3 y  = - 10                        ………..(1)

Ten years later,

Age of Nuri  = x + 10

Age of Sonu = y + 10

Nuri will be twice as old as Sonu.

X+ 10 = 2(y+10)

X + 10  = 2y + 20

X – 2y  = 10                           ………..(2)

X – 3 y  = - 10                        ………..(1)

Subtracting equation (1) from equation (2)  we get

Y  = 20

Plug this value in equation first we get

X  - 3* 20 = -10

X = 60 – 10

X  = 50

Hence age  of Nuri = 50 years and age of Sonu  = 20 years

Answer 2

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

The age of Sonu is 20 years and Nuri is 50 years.

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

5 years ago = Nuri was thrice as old ae Sonu.

10 years later = Nuri will be twice as old as sonu

To find :

Ages of Nuri and Sonu

Solution :

Consider the age of Sonu as x

Consider the age of Nuri as y

The Ages 5 years ago =

Sonu = x - 5

Nuri = y - 5

Nuri was Thrice the age of Sonu (5 years before)

★ $\boxed{\sf{y-5 = 3(x-5)}}$

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

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

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

$\bf{\implies} \: y = 3x - 10 \: ............[1]$

$\rule{300}{1.5}$

10 years later :

Sonu's age = x + 10

Nuri's age = y + 10

Nuri will be twice as old as sonu.

★ $\boxed{\sf{y+10= 2(x+10)}}$

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

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

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

$\bf{\implies} \:y = 2x + 10 \: ............[2]$

$\rule{300}{1.5}$

From Equation 1 and 2 =

$\sf{\implies} \: 3x - 10 = 2x + 10$

$\sf{\implies} \: 3x - 2x = 10 + 10$

$\sf{\implies} \: x = 20$

$\rule{300}{1.5}$

Now, put the value of x in Equation 1

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

$\sf{\implies} \: y = 60 - 10$

$\sf{\implies} \:y = 50$

x = 20

y = 50

$\therefore$ The age of Sonu is 20 years and Nuri is 50 years.