 Hello and welcome to the session. The given question says two years ago a father was five times as old as a son. Two years later his age will be eight more than three times the age of the son find the present ages of father and son. Now move on to the solution and firstly let us interpret the given question in the form of a rough figure. Suppose on this line this point represents the present age of father and son and let the present age of father be x years and that of the son be y years. Now according to the question two years ago so this represents the present age so two years ago suppose this point represents the time which is two years ago so here the age of father is equal to x minus two years at age of son will be y minus two years but says two years ago father was five times as old as his son so two years ago father's age is x minus two and son's age is y minus two so according to the question the first equation as the father's age is five times the age of his son which is y minus two so let this be equation number one. Now it further says two years later so two years later suppose this point represents the time which is two years later so here the age of father will be equal to x plus two years and the age of son is equal to y plus two years now according to the question two years later father's age will be eight more than three times the age of the son so the second equation as father's age which is x plus two is eight more than three times the age of son so age of son two years later is y plus two plus eight let this be equation number two now we shall be solving Boobies equation to get the values of x and y which are the present age of father and son now let us first solve the first equation so this implies x minus five y is equal to minus eight let this be equation number three and on solving this equation we have x minus three y is equal to twelve let this be equation number four now on subtracting the fourth equation from the third equation to get the value of y here we have minus two y since x cancels out with minus x and here we have minus twenty and this we get when we subtract the fourth equation from the third equation so this implies that y is equal to ten therefore son's age is equal to ten years now substituting the value of y which is equal to ten in equation number three we have x minus five into ten is equal to minus eight or x is equal to fifty minus eight which is equal to forty two therefore the value of x which is the present age of father is forty two years hence our answer is that age of father which we had assumed as x is equal to forty two years and present age of son is equal to ten years so this completes the session hope you have understood it bye and take care