Question

027. Two years ago a man was 6 times as old as his son. After 18 years he will be twice as old as his son.What will be the preseent age of the father and the son​

Answer 1

Answer:

let the age of son, two years ago be x

so the age of man two years ago = 6x

so, present age of son = x+2

present age of man = 6x+2

now, after 18 years,

age of son = x+2+18 = x+20

age of man = 6x+2+18 = 6x+20

A2Q, 6x+20 = twice of x+20

6x+20 = 2[x+20]

6x+20 = 2x+40

6x-2x= 40-20

4x = 20

x = 20/4

x = 5

so, present age of son = x+2 = 5+2 = 7

present age of man = 6x+2 = 6*5+2 = 32

hope it helps

have a nice day

Answer 2

Given,

• Two years ago a man was 6 times as old as his son.
• After 18 years he will be twice as old as his son.

To Find,

• The Present age of father = ?
• The Present age of son = ?

Solution,

$\sf{Suppose \ the \ Present \ age \ of \ man \ be \ "a" \ years}$

$\sf{And,\ Suppose \ the \ Present \ age \ of \ his \ son \ be \ "b" \ years}$

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

• $\sf{Two \ years \ ago \ a \ man \ was \ 6 \ times \ as \ old \ as \ his \ son}$

$\implies \sf{(a - 2) = 6(b - 2)}$

$\implies \sf{a - 2 = 6b - 12}$

$\implies \sf{a - 6b = - 12 + 2}$

$\implies \sf{a - 6b = -10}$

$\implies \boxed{\sf{a = 6b - 10}}$

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

• $\sf{After \ 18 \ years \ he \ will \ be \ twice \ as \ old \ as \ his \ son.}$

$\implies \sf{(a + 18) = 2(b + 18)}$

$\implies \sf{a + 18 = 2b + 36}$

$\implies \sf{a - 2b = 36 - 18}$

$\implies \sf{a - 2b = 18}$

$\implies \sf{6b - 10 - 2b = 18}$

(Put the Value of a From the First Condition)

$\implies \sf{4b = 18 + 10}$

$\implies \sf{4b = 28}$

$\implies \sf{b = \dfrac{28}{4}}$

$\implies \boxed{\sf{b = 7}}$

$\leadsto \underline{\sf{\red{Now, \ Put \ the \ Value \ of \ b \ in \ First \ Condition:}}}$

$\implies \sf{a = 6b - 10}$

$\implies \sf{a = 6(7) - 10}$

$\implies \sf{a = 42 - 10}$

$\implies \boxed{\sf{\pink{a = 32}}}$

Therefore,

$\boxed{\bold{\purple{The \ Present \ age \ of \ man \ is \ 32 \ years}}}$

$\boxed{\bold{\red{The \ Present \ age \ of \ his \ son \ is \ 7 \ years}}}$

$\rule{200}2$