 Hello and welcome to the session. In this session we discuss the falling question which says the sum of present ages of father and his son is 54 years. Eight years later, the age of father becomes two and a half times the age of his son. Find the present ages. Let's move on to the solution now. First of all, let the present age of father be equal to x years and let the present age of son be equal to y years. Now, according to the question, we are given one condition that the sum of present ages of father and son is 54 years. So we have x plus y is equal to 54. Let this be equation one. Now, eight years later, age of father would be equal to x plus eight years and age of son would be equal to y plus eight years. Now, from the question we have that eight years later the age of father becomes two and a half times the age of his son. So now, according to the question age of the father eight years later that is x plus eight is two and a half times the age of his son eight years later that is y plus eight. So we have x plus eight is equal to five upon two multiplied by y plus eight. So further we have two multiplied by x plus eight is equal to five multiplied by y plus eight. That is we have cross multiplied. This gives us two x plus sixteen is equal to five y plus forty. Now, bringing the terms containing the variables to the left hand side and all the constants to the right hand side we get two x minus five y is equal to forty minus sixteen. That is two x minus five y is equal to twenty four. Let this be equation two. So now we have two equations with us equation one and equation two. That is x plus y equal to fifty four is equation one and two x minus five y is equal to twenty four is equation two. Now we can solve these two equations to get the values for x and y. Now we multiply the equation one by two. So we get two x plus two y is equal to hundred and eight. Now subtracting these two equations we have minus seven y is equal to twenty four minus hundred and eight. That is minus seven y is equal to minus eighty four. Now to get the value for y we divide both sides by minus seven. Now minus seven cancels with minus seven minus cancels with minus and seven twelve times is eighty four. Thus we get y is equal to twelve. Now to get the value for x we would substitute the value for y in equation one. So we have substituting y equal to twelve in equation one we get x plus twelve is equal to fifty four. That is x is equal to fifty four minus twelve which gives us the value for x as forty two. So this is the value of x and this is the value for y. And we had assumed x to be the present age of father and y to be present age of son. So thus we now have the present ages of father and son. That is we say that the present age of father is forty two years and present age of son is twelve years. So this is our final answer. This completes the session. Hope you have understood the solution of this question.