Question

Two years ago, Rahul was thrice as old as his son and six years later he will be four years older than twice his son's age. Taking present age of Rahul as x years and his son's as y years , algebraic representation of this situation will be
(2 Points)

3x-y=4 ; 2x-y=10

3x-y= -4 ; x-2y= -10

3y-x=4 ; x-2y=10

None of the above​

Answer 1

Answer:

hey here is your solution

pls mark it as brainliest

so here we go

Step-by-step explanation:

now let age of rahul be x years and his son be y years

so according to first condition

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

ie x-2=3y-6

ie x-3y=-4 (1)

according to second condition

(x+6)=4+2(y+6)

ie x+6=4+2y+12

x-2y=16-6

x-2y=10 (2)

hence option c ie 3y-x=4 and x-2y=10 is right

u can bet on it

solve the equations you would get

x=38 & y=14

and substitute it in formed equations and then verify

Answer 2

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

(3) 3y-x=4 ; x-2y=10 is correct answer

$\large\underline\mathfrak\red{Solving \: :- }$

Let the age of Rahul be x and the age of his son be y.

Then two years back their ages are

x - 2 and y - 2 respectively.

$\sf\therefore{ \: by \: the \: given \: condition}$

$\sf\implies{x - 2 = 3(y - 2)} \: \: \: \: \\ \sf\implies{x - 3y = - 4 \: \: \: ...(i)}$

Again six years later their ages will be

x + 6 and y + 6 respectively.

$\sf\therefore{ \: by \: the \: given \: condition}$

$\sf\implies{x + 6 = 2(y + 6) + 4} \\ \sf\implies{x - 2y = 10 \: \: \: ...(ii)} \: \: \: \:$

Finding x

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

Putting x = 10 + 2y in equation (i)

$\sf\implies{x - 3y = - 4} \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf\implies{10 + 2y - 3y = - 4} \\\sf\implies{10 - y = - 4} \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf\implies{10 + 4 = y} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf\implies{y = 14} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

${\large{\underline{\boxed{\sf{\red{y = 14 }}}}}}$

Putting y = -14 in equation (II)

$\sf\implies{x - 2y = 10} \: \: \: \: \: \: \: \: \: \: \: \\ \sf\implies{x - 2(14) = 10} \: \: \: \: \: \: \\ \sf\implies{x - 28 = 10} \: \: \: \: \: \: \: \: \: \: \: \\ \sf\implies{x = 10 + 28 = 38}$

${\large{\underline{\boxed{\sf{\red{x = 38 }}}}}}$

Answer :

Rahul age is 38 years

His son's age is 14 years

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