Question

Age of father is twice the sum of ages of his two children. Ten years hence the age of father will be three quarter of the sum of ages of his children then Find the present age of father

Answer 1

Let age of father be F years.

Let age of two children be x and y.

According to question:

1. Age of father is twice the sum of ages of his two children.

$F = 2 \times (x+y) \\\Rightarrow (x+y) = \dfrac{F}{2} ...... (1)$

2. Ten years hence the age of father will be three quarter of the sum of ages of his children.

Ten years hence, age of father = F + 10

Ten years hence, age of children = (x + 10) and (y + 10)

As per the given statement:

$F+10 = \dfrac{3}{4} (x+10+y+10)\\\Rightarrow F+10 = \dfrac{3}{4} (x+y+20)\\\Rightarrow 4(F+10) = 3 \times (x+y+20)$

Using equation (1) to put the value of (x+y) :

$\Rightarrow 4(F+10) = 3 \times (\dfrac{F}{2}+20)\\\Rightarrow 4(F+10) = 3 \times (\dfrac{F+40}{2})\\\Rightarrow 4 \times 2(F+10) = 3 \times (F+40)\\\Rightarrow 8F+80 = 3F+120\\\Rightarrow 5F = 40\\\Rightarrow F = 8$

So, present age of father = 8 years