 Hello and welcome to the session. In this session we discussed the following question which says, a chemist has solution A containing 60% acid and a solution B containing 40% acid. How much of each should be used to make 10 liters of a 50% acid solution? So in this question we need to find the amount of solution A and solution B that need to be mixed to make 10 liters of a 50% acid solution. So let's see its solution now. First of all we assume that x liters of solution A be mixed with y liters of solution B. And so this would mean x plus y is equal to 10. That is if x liters of solution A is mixed with y liters of solution B then we get 10 liters of a solution. Let this be equation 1. Next let's find out the quantity of acid in x liters of solution A. This would be equal to 60% of x liters since we have that a solution A contains 60% acid. So this is equal to x into 60 upon 100 liters. So this is equal to 60x upon 100 liters. So quantity of acid in x liters of solution A is 60x upon 100 liters. Next we find out the quantity of acid in y liters of solution B and this would be equal to 40% of y liters since we know that solution B contains 40% acid. So the quantity of acid in y liters of solution B is equal to 40% of y liters. That is equal to y into 40 upon 100 liters or this is equal to 40y upon 100 liters is the acid in y liters of solution B. Next let's find out the quantity of acid in 10 liters of solution A and solution B and we need to make 10 liters of a 50% acid solution. So quantity of acid in 10 liters of solution A and solution B is equal to 50% of 10 liters. That is equal to 50 upon 100 into 10 liters or you can say this is equal to 5 liters. Now the equation that we get from all these results is quantity of acid in x liters of solution A that is 60x upon 100 liters, 60x upon 100 plus the quantity of acid in y liters of solution B that is 40y upon 100 is equal to quantity of acid in 10 liters of solution A and solution B is equal to 5. So this gives us 60x plus 40y is equal to 500 or you can say 6x plus 4y is equal to 50. Now taking 2 common inside the bracket we get 3x plus 2y is equal to 50. This further gives us 3x plus 2y is equal to 50 upon 2 that is 25. Let this be equation 2. So now we get 2 equations x plus y equal to 10 that is equation 1 and 3x plus 2y is equal to 25. This is equation 2. Now we solve equations 1 and 2 to get the values for x and y. So for this we multiply equation 1 by 3 so multiplying equation 1 by 3 we get 3x plus 3y is equal to 30. Let this be equation 3 and now the equation 2 is 3x plus 2y is equal to 25. Now subtracting equation 2 from equation 3 we get 3x plus 3y minus 3x plus 2y is equal to 30 minus 25. This gives us 3x plus 3y minus 3x minus 2y is equal to 5. Now 3x and minus 3x cancels 3y minus 2y is y this is equal to 5. To get the value of x we need to substitute y equal to 5 in equation 1. So substituting y equal to 5 in equation 1 we get x plus y equal to 10 that is x plus 5 equal to 10 which means we get x is equal to 10 minus 5 that is equal to 5. So x is equal to 5 and y is equal to 5. So this means 5 liters of solution A would be mixed with 5 liters of solution B to make 10 liters of a 50% acid solution. So 5 liters of solution A and 5 liters of solution B are needed. This is our final answer. So this completes the session. Hope you have understood the solution for this question.