Question

Two years ago, a man was five times as old as his son. two years later, his age will be 8 more than three times the age of son. find the present ages of a man and his son.

Answer 1

let the man's age=x
let the son's age=y

x-2=5(y-2)
x-2=5y-10
x-5y=-8

x+2=8+3(y+2)
x+2=8+3y+6
x+2=14+3y
x-3y=12

compare both the equations
-2y=-20
y=10

x-30=12
x=42

so the age of man=42
so the age of son=10

Answer 2

Given,

• Two Years ago . A man was five times as old his son.
• Two Years later , his age will be 8 more than three times the age of son.

To Find,

• The Present age of man
• The Present age of son

Solution :

$\implies$ Suppose the Present age of man be a years

And, Suppose the Present age of son be b years

$\mapsto \underline{\sf{\pink{According \ to \ the \ First \ Condition :}}}$

• Two Years ago . A man was five times as old his son.

$\implies \sf{a - 2 = 5(b - 2)}$

$\implies \sf{a - 2 = 5b - 10}$

$\implies \sf{a - 5b = -10 + 2}$

$\implies \sf{a - 5b = -8}$

$\implies \boxed{\sf{a = -8 + 5b}}$   1) Equation

$\mapsto \underline{\sf{\pink{According \ to \ the \ Second \ Condition :}}}$

• Two Years later , his age will be 8 more than three times the age of son.

$\implies \sf{a + 2 = 3(b + 2) + 8}$

$\implies \sf{a + 2 = 3b + 6 + 8}$

$\implies \sf{a + 2 = 3b + 14}$

$\implies \sf{a - 3b = 14 - 2}$

$\implies \sf{a - 3b = 12}$

║Now Put the Value of a From the First Equation ║

$\implies \sf{-8 + 5b - 3b = 12}$

$\implies \sf{2b = 12 + 8}$

$\implies \sf{2b = 20}$

$\implies \sf{b = \dfrac{20}{2}}$

$\implies \boxed{\sf{b = 10}}$

║Now Put the Value of b in First Equation ║

$\implies \sf{a = -8 + 5b}$

$\implies \sf{a = -8 + 5(10)}$

$\implies \sf{a = -8 + 50}$

$\implies \boxed{\sf{a = 42}}$

Therefore,

$\large{\boxed{\bold{\red{Present\:age\:of\:man\:=\:a\:=\:42\:years}}}}$

$\large{\boxed{\bold{\purple{Present\:age\:of\:son\:=\:b\:=\:10\:years}}}}$

$\rule{200}2$