Question

Five years hence, the age of father will be 10 years more than twice the age of the son. Taking the present age of father and son as x and y years respectively, then the linear equation representing the above situation is

a. x - 2y - 25 = 0
b. x - 2y - 20 = 0
c. x - 2y - 15 = 0
d. 2x - y + 15 = 0

Answer 1

Given :

• Five years hence, the age of father will be 10 years more than twice the age of the son.
• The present age of father and son as x and y years respectively.

To find :

• Linear equation representing the above situation.

Solution :

• Present age of father = x years
• Present age of son = y years

After 5 years,

• Age of father = (x+5) years
• Age of son = (y+5) years

According to the question :-

• Five years hence, the age of father will be 10 years more than twice the age of the son.

$\implies\sf{x+5=2(y+5)+10}$

$\implies\sf{x+5=2y+10+10}$

$\implies\sf{x+5=2y+20}$

$\implies\sf{x-2y+5-20=0}$

$\implies\sf{x-2y-15=0}$

Therefore, the required linear equation representing the above situation is x-2y-15 = 0.

Hence,

Correct answer is option (c).

Answer 2

$\huge \mathfrak{Answer:-}$

$\implies$ x - 2y - 15 = 0

$\large\underline\mathrm{Given:-}$

• Five years hence, the age of father will be 10 years more than twice the age of the son.
• The present age of father and son as x and y years respectively.

$\large\underline\mathrm{Solution}$

• present age of father = x year's
• present age of son = y year's

$\large\underline\mathrm{After \: 5 \: year's}$

• Age of father = x + 5 year's
• Age of son = y + 5 year's

$\large\underline\mathrm{According \: to \: the \: questions}$

• Five years hence, the age of father will be 10 years more than twice the age of the son.

$\implies$ x + 5 = 2(y + 5) + 10 = 0

$\implies$ x + 5 = 2y + 10 + 10 = 0

$\implies$ x + 5 = 2y + 20 = 0

$\implies$ x - 2y + 5 - 20 = 0

$\implies$ x - 2y - 15 = 0

$\large\underline\mathrm{hence,}$

$\large\underline\mathrm{the \: required \: linear \: equations \: respecting \: the \: above \: situation \: is \: x \: - \: 2y \: - \: 15 \: = \: 0.</p><p>}$

$\large\underline\mathrm{Hope \: it \: helps \: you \: plz \: mark \: me \: brainlist}$