 Hello and welcome to the session. In this session we discuss the question which says that two pipes running together can fill a tank in 111 by 9 minutes. If one pipe takes 5 minutes more than the other to fill the tank separately, find the tank in which each pipe would fill the tank separately. And now we will start with the solution. Now let the first pipe fill the tank in. Now it is given in the question that one pipe takes 5 minutes more than the other to fill the tank separately. Therefore, the second pipe can fill the tank in x plus 5 minutes. Now as the first pipe can fill the tank in x minutes, so now two of tank first pipe is equal to 1 by x. Now it is given that the two pipes running together can fill the tank in 111 by 9 minutes. So now let the tank first pipe 111 by 9 minutes that is equal to 100 by 9 into 1 by x. This is equal to 100 by 9x. So this is pushing of the tank filled by the first pipe in 11 and 1 by 9 minutes which is equal to 100 by 9 into pushing of the tank filled by the first pipe in 1 minute. The first pipe of the tank filled by the second pipe in 9 minutes that is equal to 100 by 9 into pushing of the tank filled by the second pipe in 1 minute that is 1 by x plus 5. That is equal to 100 over 9 into x plus 5 the whole. Now it is given that the two pipes running together can fill the tank in 11 and 1 by 9 minutes. So this is the portion of the tank filled by the first pipe in 11 and 1 by 9 minutes. Now the tank filled by the second pipe in 11 and 1 by 9 minutes. Now it is given filling the tank 11 and 1 by 9 minutes that is 100 by 9 by the first pipe in 100 by 9 minutes. 100 by 9 into x plus 5 the whole that is portion of the tank filled by the second pipe in 100 by 9 minutes is equal to 1. Now this implies taking 100 by 9 common it will be 100 by 9 into 1 by x plus 1 by x plus 5 the whole is equal to 1. Now this implies 100 by 9 into on taking the portion it will be x into x plus 5 the whole and in the numerator it will be x plus 5 the whole is equal to 1. This further implies is equal to 9 by 100. Now on first multiplying this implies 200 is equal to 9x square plus 45x. This implies 9x square plus 45x minus 200x minus 500 is equal to 0. This further implies 9x square minus 155x minus 500 is equal to 0. Now this is a quadratic equation in x so by splitting the middle term it will be 9x square minus 180x plus 25x minus 500 is equal to 0. Now from these three terms taking 9x common this implies 9x into x minus 20 the whole and from these two terms taking 25 common it will be plus 25 into x minus 20 the whole is equal to 0. Which further implies 9x plus 25 the whole into x minus 20 the whole is equal to 0. Now this implies either 9x plus 25 is equal to 0 or x minus 20 is equal to 0. Which further implies 9x is equal to minus 25 or x is equal to 20 and this implies x is equal to minus 25 by 9 or x is equal to 20. Now here x minutes is the time taken by the first five to fill the tank. So as not be negative is equal to 20 that is x is equal to 20 minutes. Confirm the tank in 20 minutes so here the second type is minutes which is equal to 20 plus 5 which is equal to 25 minutes. This is the solution of the given question and that's all for this session. Hope you all have enjoyed this session.