Question

Father's age is three times the sum of ages of his two children. After $5$ years his age will be twice the sum of ages of two children. Find the age of father.

• A. Father's age $=75$ years
• B. Father's age $=45$ years
• C. Father's age $=66$ years
• D. Father's age $=88$ years

Answer 1

Answer: (B)

Let the age of father $=x$ years
The sum of the age of $2$ children $=y$ years
According to the first condition
$\Rightarrow x=3y.....eq1$
After $5$ years
$\Rightarrow$ Father's age $=x+5$
$\Rightarrow$ The sum of ages of his two children $=y+10$

According to the second condition
$\Rightarrow x+5=2(y+10)\Rightarrow x+5=2y+20$
$\Rightarrow x-2y=\mathrm{15....}eq2$
Put the value of $x$ from $eq1$
$\Rightarrow 3y-2y=15\Rightarrow y=15$
Put $y=15$ in $eq1$
$\Rightarrow x=3\times 15\Rightarrow x=45$

Hence, father age $=45$ years