 Welcome to my name is Mansi and I am going to help you with the following question. The question says a solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting mixture is to be more than 4% but less than 6% boric acid. If we have 640 litres of the 8% solution, how many litres of the 2% solution will have to be added? Let us into this question. We see that quantity of 8% boric acid solution given is equal to 640 litres. Now quantity of 2% boric acid solution added be equal to x litres then the total quantity of mixture is equal to 640 plus x litres. Now as the boric acid contains in the mixture should be more than 4% but less than 6% therefore according to the two given conditions first 8% of 640 plus 2% of x is strictly greater than 4% of 640 plus x and second is 8% of 640 plus 2% of x is strictly less than 6% of 640 plus x. Now inequality is 8% of 640 plus 2% of x is strictly greater than 4% of 640 plus x or we can say 5120 plus 2x is strictly greater than 4x plus 2560 or 2x is strictly greater than 4x minus 2560 or minus 2x is strictly greater than minus 2560 or x is strictly less than 1280. Now we see is 8% of 640 plus 2% of x is strictly less than 6% of 640 plus x or 8 into 6.40 plus 0.02 of x is strictly less than 0.06 into 640 plus x or 5120 plus 2x is strictly less than 3840 plus 6x or 2x is strictly less than 6x minus 1280 or minus 4x is strictly less than minus 1280 or x is strictly greater than 320. So from the solutions of inequalities 1 and 2 we conclude that 320 is strictly less than x which is strictly less than 1280 therefore required quantity is more than 320 liters but less than 1280 liters and this is also our answer to this question. I hope you understood the question and enjoyed the session have a good day.