 Hello and welcome to the session. In this session we discuss the following question which says the present age of a girl is 4 years more than 3 times the age of a boy. 2 years hence the girl's age will be 6 years more than twice the age of the boy. Find their present ages. So in this question we need to find the present age of the boy and the girl and we are given some conditions in the question. So let's see solution now. First of all we assume let the present age of the girl be equal to x years and also we assume the present age of the boy be equal to y years. So in the question we are given one condition. So according to the question we have that the present age of a girl is 4 years more than 3 times the age of the boy. So this means that the present age of the girl which is x is 4 more than 3 times the age of the boy that is x is equal to 3 y plus 4. This means x minus 3 y is equal to 4. Let this be equation 1. Now next we find out 2 years hence the age of the girl would be equal to present age plus 2 that is x plus 2 years. Then 2 years hence the age of the boy is equal to present age of the boy that is y plus 2 that is y plus 2 years. Now we have another condition given in the question. So according to the question we have that the 2 years hence the girl's age will be 6 years more than twice the age of the boy. This means that x plus 2 would be equal to twice the age of the boy which is 2 into y plus 2 plus 6. This means x plus 2 is equal to 2 y plus 4 plus 6. Or you can say x minus 2 y is equal to 10 minus 2 that is we get x minus 2 y is equal to 8. Let this be equation 2. So we have now got 2 equations x minus 3 y equal to 4 which is equation 1 and x minus 2 y equal to 8 which is equation 2. Now we will solve both these equations for the values of x and y. Now subtracting equation 2 from equation 1 we get x minus 3 y minus x minus 2 y is equal to 4 minus 8. That is we have x minus 3 y minus x plus 2 y is equal to minus 4. x minus x cancels here we have minus y is equal to minus 4 or you can say y is equal to 4. We have got the value for y now substituting y equal to 4 in equation 1 we get this is the equation 1 x minus 3 y equal to 4. So we will put y equal to 4. Now we have x minus 3 into 4 is equal to 4 that is x minus 12 equal to 4 which gives us x is equal to 16. So we have now got x equal to 16 and y equal to 4. And as you know that we had assumed x to be the present age of the girl and y to be the present age of the boy. So now we can say the present age of the girl is equal to 16 years and the present age of the boy is equal to 4 years. So this is our final answer. With this we complete the session. Hope you have understood the solution of this question.