Question

Sam's present age is two-fifth
of the age of his mother, 6 years hence, he will be half of
the age of his mother. What is the present age of his mother? ​

Answer 1

Answer:

LET SAM'S MOTHER AGE IS "X"

THEN, SAMS AGE IS 2/5 OF X after 6 years age of mother is X + 6 then age of Sam is half of X + 6

2/5(x)+6 = 1/2(x+6)

2x/5+6 = x/2+3

2x/5-x/2 = -3

4x/10-5x/10 = -3

-x/10 = -3

x/10 = 3

x = 30

Answer 2

Step-by-step explanation:

$\bf\underline{\underline{\red{Given:-}}}$

• Sam's present age is two-fifth of the age of his mother.

• 6 years hence, Sam will be half of the age of his mother.

$\bf\underline{\underline{\blue{To\:Find:-}}}$

• The present age of his mother.

$\bf\underline{\underline{\green{Solution:-}}}$

Case 1:-

Let the present age of his mother be x

As, Sam's present age is two- fifth of the age of his mother

Present age of Sam = ⅖ x

Case 2:-

6 years hence (later):-

$\rm Age \: of \: his \: mother = x + 6$

$\rm Age \: of \: Sam = \dfrac{2x}{5} + 6$

Given, Sam will be half of the age of his mother.

$\rm \implies \dfrac{1}{2} \big( x + 6 \big)= \dfrac{2x}{5} + 6$

$\rm \implies \dfrac{x + 6 }{2}= \dfrac{2x + 30}{5}$

$\rm \implies {5(x + 6 )}= {2(2x + 30)}$

$\rm \implies {5x + 30}= {4x + 60}$

$\rm \implies {5x - 4x}= { 60 - 30}$

$\rm \implies {x}= { 30}$

Present age of his mother = x = 30

$\underline{\boxed{\purple{\rm \therefore Present \: of \: his \: mother = 30 \: years}}}$