Question

Ram is elder than Sam's 2year before 10year shyam and ram ratio is 1:2..how old r ram now?

Answer 1

$\Large{\underline{\underline{\mathfrak{\bf{Question}}}}}$

Ram is elder than Sam's 2 year . Before 10year shyam and ram ratio is 1:2 .how old r ram now ?

$\Large{\underline{\underline{\mathfrak{\bf{Solution}}}}}$

$\Large{\underline{\mathfrak{\bf{\pink{Given}}}}}$

• Ram is elder than Sam's 2 year
• Before 10year shyam and ram ratio is 1:2

$\Large{\underline{\mathfrak{\bf{\pink{Find}}}}}$

• Age of Ram and Shyam

$\Large{\underline{\underline{\mathfrak{\bf{Explanation}}}}}$

Let,

• Age of Ram be = x years
• Age of Shyam be = y years

A/C to question,

( Ram is elder than Shyam's 2 year )

➥ x = y + 2

➥ x - y = 2 .........(1)

Again,

( Before 10year shyam and ram ratio is 1:2 )

➥ (x-10) : (y-10) = 1:2

Write in Division form ,

➥ (x-10)/(y-10) = 1/2

➥ 2(x-10) = (y-10)

➥ 2x - y = -10 + 20

➥ 2x - y = 10 ........(2)

Multiply by 2 in equ(1)

• 2x - 2y = 4

And,

• 2x - y = 10

_____________Sub. it's

➥ (-2y +y) = (4-10)

➥ -y = -6

➥ y = 6

Keep value of y in equ(1),

➥ x - 6 = 2

➥ x = 2 + 6

➥ x = 8

_______________________

Hence:-

• Age of Ram will be = 8 years
• Age of Shyam will be = 6 years

________________________

$\Large{\underline{\mathfrak{\bf{\blue{Answer\:Verification}}}}}$

( Ram is elder than Sam's 2 year )

➥ x = y + 2

Keep value of x and y,

➥ 8 = 6 + 2

➥ 8 = 8

L.H.S. = R.H.S.

Again,

( Before 10year shyam and ram ratio is 1:2 )

➥ (x-10):(y-10) = 1:2

➥ (x-10)/(y-10) = 1/2

keep value of x and y

➥ (8-10)/6-10) = 1/2

➥ (-2)/(-4) = 1/2

➥ 1/2 = 1/2

➥ 1:2 = 1:2

L.H.S = R.H.S

Here, proved both condition

So, we can say that our solution is right .

____________________

Answer 2

$\large{\underline{\red{\rm{AnswEr:8\: years}}}}$

$\bold\orange{\underline{Correct\:Question:}}$

The age of Ram is 2 years older than the age of Shayam.10 years,ago the ratio of their age will be 1:2.Find the present age of Ram.

$\bold\purple{\underline{Let:}}$

The present age of Ram=X

The present age of Shayam=Y

$\bold\red{\underline{A.T.Q}}$

The age of Ram is 2 years older than

Shayam

⟹X=Y+2

⟹X-Y=2

⋆$\bold\purple{\boxed{X-Y=2-------(i)}}$

10 years ago the ratio of their age will be 1:2

⟹X-10/Y-10=1/2

⟹2X-20=Y-10

⟹2X-Y=-10+20

⟹2X-Y=10

⋆$\bold\purple{\boxed{2X-Y=10------(ii)}}$

Solving equations 1 and 2 by multiplying and subtracting in EQ 1 multiplying by 2 and EQ 2 by 1

⟼2X-2Y=4---------(iii)

⟼2X-Y=10----------(iv)

⟼-Y=-6

⟼Y=6

Putting the value of y=6 in EQ 1

⟼X-Y=2

⟼X-6=2

⟼X=8

Hence,

The present age of Ram=8years

The present age of Shayam=6years