Question

The present ageof father is 3 times of sum of ages of his two sons. Five years later he will be twice
the sum of ages of his two sons. Find the present age of the father
explain ​

Answer 1

Given :-

The present age of father = Sum of ages of his two sons × 3

Age of the father five years later = Sum of ages of his two sons × 2

To Find :-

The present age of the father.

Solution :-

Let the age of father be x years and sum of the ages of his sons be y years.

Then after 5 years,

Father's age = (x + 5) years

Sum of ages of his sons = (y + 10) years

According to the question,

$\longrightarrow \sf x = 3y \qquad ...(1)$

And, $\sf x + 5 = 2(y + 10)$

$\longrightarrow \sf x-2y=15 \qquad ...(2)$

From equation (1) and (2), we have,

$\implies \sf (3x+5)=2(x+10)$

$\sf =(3x+5)=2x+20$

$\sf =x=15$

Hence,

$\sf 3x=3(15)=45$

Therefore, the present age of father is 45 years.