 Hello and welcome to the session. My name is Mansi and I am going to help you with the following question. The question says how many liters of water will have to be added to 1, 1, 2, 5 liters of the 45% solution of acids so that the resulting mixture will contain more than 25% but less than 30% acid content. So let us start with a solution to this question. It is given that quantity of 45% solution of acid given is 1, 1, 2, 5 liters. Now let the quantity of water added be x liters then the total quantity of mixture will be quantity of 45% solution of acid plus quantity of water added that is 1, 1, 2, 5 plus x liters. Now total acid content in the mixture is equal to 45% of 1, 1, 2, 5 that is the acid content according to given conditions we get two inequalities. First is 45% of 1, 1, 2, 5 that is total acid content in the mixture is greater than 25% of 1, 1, 2, 5 plus x and second is 45% of 1, 1, 2, 5 is less than 30% of 1, 1, 2, 5 plus x. Now we need to solve these two inequalities. So first of all let us consider the first inequality that is 45% of 1, 1, 2, 5 is greater than 25% of 1, 1, 2, 5 plus x or 0.45 into 1, 1, 2, 5 is greater than 0.25 multiplied with 1, 1, 2, 5 gives 281.25 plus 0.25x. Now we can multiply both the sides by 100 and that gives us 506.25 is greater than 0.25 multiplied with 1, 1, 2, 5 gives 281.25 plus 0.25x. Now we can multiply both the sides by 100 and that gives us 506.25 is greater than 281.25 plus 25x. This implies 506.25 minus 281.25 is greater than 25x. This minus this gives us 22500 is strictly greater than 25x. Now on dividing both the sides by 25 we get 22500 by 25 is greater than 25x by 25. This side if we divide this by 25 we get 900. Here we see 25 gets cancelled from numerator and denominator we are left with x. So we have x is less than 900. Now let us solve the second inequality that is 45% of 1, 1, 2, 5 is less than 30% of 1, 1, 2, 5 plus x or 0.45 into 1, 1, 2, 5 is less than 0.30 into 1, 1, 2, 5 plus x. On multiplying 0.45 with 1, 1, 2, 5 we get 502.65 is less than 0.30 into 1, 1, 2, 5 is 337.50 plus 0.30x. Now we can multiply throughout by 100 we get 50265 is less than 33750 plus 30x or 50265 minus 33750 gives us 16875 is less than 30x. Now let us divide both the sides by 30 so we'll have 16875 by 30 is less than 30x by 30. Now here if we divide this numerator and denominator by 30 so in the numerator we'll have 1 and in the denominator we'll have 562.5 here 30 gets cancelled with 30 and we have 562.5 is strictly less than x. Now from these two inequalities that is x is less than 900 and x is greater than 562.5 we get 562.5 is less than x is less than 900 therefore required quantity of water is more than 562.5 liters but less than 900 liters. So I hope that you understood the question and enjoyed the session. Have a good day.