 Hello and welcome to the session. In this session we discuss the following question it says divide $215 among A, B and C so that A's share may be to B's share as 2 is to 5 and B's share may be to C's share as 4 is to 3. Let's proceed with the solution now we are given ratio of A's share to B's share is equal to 2 is to 5 and ratio of B's share to C's share is equal to 4 is to 3 that is we have A upon B as 2 upon 5 and B upon C is equal to 4 upon 3. Now we make the consequent of the first ratio that is A is to B which is 5 equal to the antecedent of the second ratio that is B upon C which is 4 that is these two terms should be equal. So for this we will find out the LCM of 5 and 4. So LCM of 5 and 4 is given as 20. Thus we will make these two terms as 20. So for this we will multiply the numerator and denominator of A upon B by 4 so that its denominator becomes 20. Thus we get A upon B equal to 8 upon 20. In the same way we multiply the numerator and denominator of the ratio B upon C by 5 so that its numerator becomes 20. Thus we now have B upon C equal to 20 upon 15. So now we find that the consequent of the first ratio is equal to the antecedent of the second ratio. Thus we have A is to B is equal to 8 is to 20 and B is to C is equal to 20 is to 15 or you can say that A is to B is to C is equal to 8 is to 20 is to 15. Now sum of the ratios is equal to 8 plus 20 plus 15 which is equal to 43. So now we can easily find out the individual shares of A, B and C. First of all let's find out A is share this would be equal to A is part which is 8 upon B sum of the ratios that is 43 multiplied by the given money which is 215 dollars. Now 43 5 times is 215 and 8 multiplied by 5 is 40 so this is equal to 40 dollars that is we have A is share is equal to 40 dollars. In the same way let's try to find out B is share which would be given by B is part that is 20 upon sum of the ratios that is 43 multiplied by the given money that is 215 dollars. Now 43 5 times is 215 and 5 multiplied by 20 is 100 so this is equal to 100 dollars. Thus we have B's share is equal to 100 dollars. Now C's share is given by C's part which is 15 upon sum of the ratios that is 43 multiplied by the given money that is 215 dollars. Now 43 5 times is 215 and 15 multiplied by 5 is 75 thus we get 75 dollars that is C's share thus we get A's share as 40 dollars B's share as 100 dollars and C's share as 75 dollars. So this completes the session hope you have understood the solution of this question.