 Hello and welcome to the session. Let us discuss the following problem today. Formulate the following problem as a pair of equations and hence find its solution. We have two women and five men can together finish an embroidery work in four days, while three women and six men can finish it in three days. Finally, time taken by one woman alone to finish the work and also the time taken by one man alone. Now let us write the solution. We have to find that how long will one woman and one man will alone finish the work? Suppose one man can finish the work in M days and one woman can finish the work in N days. Therefore one man's one day's work is equal to 1 by M and one woman's one day work is equal to 1 by N. Therefore five men's one day's work is equal to 5 by M and two women's one day's work is equal to 2 by N. Now five men's and two women's one day's work is equal to 5 by N plus 2 by N and five men's and two women's one day's work is equal to 4 into 5 by M plus 2 by N is equal to 1, which implies 5 by M plus 2 by N is equal to 1 by 4. Now according to the question six men and three women can finish the work in three days. Therefore six men's one day's work is equal to 6 by M and three women's one day's work is equal to 3 by N. Now six men's and three women's one day's work is equal to 6 by M plus 3 by N. Now six men's and three women's three days work is equal to 3 into 6 by M plus 3 by N is equal to 1 or 6 by M plus 3 by N is equal to 1 by 3. So we have got the two equation which are 20 by M plus 8 by N is equal to 1 and 18 by M plus 9 by N is equal to 1. Let us name these equations as 1 and 2. Now let 1 by M is equal to X and 1 by Y is equal to Y. Therefore we get 20 X plus 8 Y is equal to 1 and 18 X plus 9 Y is equal to 1. Let us name these as 3 and 4. Now using cross multiplication method we get A1 is equal to 20, A2 is equal to 18, V1 is equal to 8, V2 is equal to 9, C1 is equal to minus 1 and C2 is equal to minus 1. Therefore X by V1 C2 minus V2 C1 is equal to Y by C1 A2 minus C2 A1 is equal to 1 by A1 V2 minus A2 B1 which implies X by 8 into minus 1 minus 9 into minus 1 is equal to Y by minus 1 into 18 minus 20 into minus 1 is equal to 1 by 20 into 9 minus 18 into 8 which implies X by minus 8 plus 9 which is equal to Y by minus 18 plus 20 which is equal to 1 by 180 minus 144 which implies X by 1 is equal to Y by 2 which is equal to 1 by 36. Now X by 1 is equal to 1 by 36 which implies 1 by 36 is equal to 1 by M because X is equal to 1 by M which implies M is equal to 36. Now similarly Y by 2 is equal to 1 by 36 which implies Y is equal to 1 by 18 which implies 1 by N is equal to 1 by 18 because Y is equal to 1 by N which implies N is equal to 18 hence two required questions are 2 by N plus 5 by M is equal to 1 by 4 and 3 by N plus 6 by M is equal to 1 by 3 where N is number of days taken by one woman and M is number of days taken by one man and N is equal to 18, M is equal to 36. I hope you understood the problem. Bye and have a nice day.