 Hello and welcome to the session, let us discuss the following question. It says, father's age is three times the sum of the ages of his two children. After five years, his age will be twice the sum of the age of two children find the age of the father. So let's now move on to the solution. We have to find the age of the father. So let father's present age be x and the sum of the ages of two children equal to y. According to question, we are given that father's age is three times the sum of the ages of his two children. That is, three times the sum of the ages of the children is equal to the father's age because we are given that father's age is three times the sum of the ages of the children. So we have x is equal to three y. Let's name this as equation one. Now according to second condition, we are given that after five years his age will be twice the sum of the age of the two children. So after five years, father's age will be x plus five years since the present age is x. So after five years, father's age will be x plus five years and the sum of ages of two children will be y plus five plus five years. Since the sum of the ages of the two children is given to be, is assumed to be y, so five years later the sum of the ages of two children will be y plus five plus five years. And in the question we are given that father's age will be twice the sum of the ages of the two children after five years. So again according to question, x plus five is twice the sum of the ages of the two children that is two into y plus five plus five that is ten. So now we'll solve this. X plus five is equal to two y plus twenty. So this implies x minus two y is equal to twenty minus five that is x minus two y is equal to fifteen. Now this equation can also be written as x minus three y is equal to zero, right? Let's name this as a and this as b. Now we'll solve equation a and b for x and y. So we'll subtract equation b from equation a. Now equation a is x minus three y is equal to zero and equation b is x minus two y is equal to fifteen. Now we have to subtract equation b from equation a. So sine will change. So plus x gets cancelled with minus x minus three y plus two y is minus y. Zero minus fifteen is minus fifteen. So this implies y is equal to fifteen cancelling minus sine on both sides. So y is equal to fifteen which is the sum of ages of two children. Now we know that father's age is three times the sum of the ages of the two children that is x is equal to three y from equation a or one. So x is equal to three into fifteen. So this implies x is equal to forty five years. So this implies father's age is forty five years. So this completes the question and the session. Do take care of all your calculations. So bye for now. Take care. Have a good day.