Question

four years ago abay's age was thrice that of his son kabir's age. 8 years later a abay's age will be twice that of kabir's age what is abay's present age​

Answer 1

let Abay's present age be x and Kabir's present age be y.

4yrs ago,

Abay's age = x-4

Kabir's age = y-4

8yrs later,

Abay's age = x+8

Kabir's age = y+8

A/q

x-4 = 4(y-4)

⇒x-4 = 4y - 16

⇒x = 4y-16+4

⇒x = 4y-12 -------- (i)

also, x+8 = 2(y+8)

⇒x+8 = 2y+16

⇒x = 2y+16-8

⇒x = 2y+8 -------- (ii)

from (i) & (ii),

4y-12 = 2y+8

⇒4y-2y = 8+12

⇒2y = 20

⇒y = 10

putting y = 10 in eq(ii)

x = 2×10+8 = 20+8 = 28

so, Abay's present age = 28yrs

Kabir's present age = 10yrs

Answer 2

$\rm\longrightarrow Let \ the \ present \ age \ of \ Abay \ be \ \bf{x} \rm \ and \ the \ present \ age \ of \ Kabir \ be \ \bf{y} \ .\\\\\rm Fours \ years \ ago \ :\\\\\rm Age \ of \ Abhay = x-4\\\\\rm Age \ of \ Kabir = y-4 \\\\\rm 8 \ years \ later \ :\\\\Age \ of \ Abhay =x+8\\\\Age \ of \ Kabir = y+8$

$\rm According \ to \ the \ first \ condition \ : \\\\\longrightarrow x-4=3(y-4) \\\\\longrightarrow x-4=3y-12\\\\\longrightarrow x-3y=-8 \ \ \ \ \ \ \ \ \ \ \ \ ................(1)\\\\\rm According \ to \ the \ second \ condition \ : \\\\\longrightarrow x+8=2(y+8)\\\\\longrightarrow x+8=2y+16\\\\\longrightarrow x-2y=8 \ \ \ \ \ \ \ \ \ \ \ \ \ \ ................(2)$

$\rm Eq(2)-Eq(1) \\\\\longrightarrow\bf\underline{ y=16}$

$\rm Substituting \ the \ value \ of \ y \ in \ Eq(1)\ : \\\\\longrightarrow x- 3\times16=-8\\\\\longrightarrow x=-8+48\\\\\longrightarrow\bf\underline{ x=40 }$

Present age of Abhay = 40 years

Present age of Kabir = 16 years

Hope it helps u .........   :)