Question

a father's age is equal to total age of three children .After 5 year the father will be only 6/7 of the total age how old is the father now?
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Answer 1

AnswEr :

Let the Total Age of 3 Children be n yrs.

• According to the Present Age :

↠ Father = Total Age of three Children

↠ n years = n years

$\rule{150}{1}$

• AFTER⠀5⠀YEARS :

$:\implies\tt Father = \dfrac{6}{7} \times Children's\:Age\\\\\\:\implies\tt (n + 5) = \dfrac{6}{7} \times [n + (3 \times 5)]\\\\\\:\implies\tt n + 5 =\dfrac{6}{7} \times [n + 15]\\\\\\:\implies\tt 7(n + 5) = 6(n + 15)\\\\\\:\implies\tt 7n + 35 = 6n = 90\\\\\\:\implies\tt 7n - 6n = 90 - 35\\\\\\:\implies \boxed{\tt n = 55 \:years}$

⠀

$\therefore\:\underline{\textsf{Present Age of Father is \textbf{55 years.}}}$

Answer 2

Step-by-step explanation:

Let father's age be $x$ years

According to the question,

Father's age = Total age of three children

So, Total age of three children = $x$ years

After 5 years,

Father's age = 6/7 × Children's age

$x+5$ = 6/7 ($x$+(3×5)) years

x+5 years = 6/7 (x + 15) years

7(x + 5) years = 6(x + 15) years

7x + 35 years = 6x + 90 years

7x-6x = 90-35 years

x = 55 years

Therefore, the father's age is x = 55 years.