 Hello and welcome to the session. I am Deepika and I am going to help you to solve the following question. The question says, the difference of two numbers is 5 and the difference of their reciprocal is 1 over 10, find the numbers. So let's start the solution. According to the question, the difference of two numbers is 5. So let the larger number be, therefore the smaller number is x minus 5. Again, we are given the difference of their reciprocal is 1 over 10. Now the reciprocal of x is 1 over x and the reciprocal of x minus 5 is 1 over x minus 5, since 1 over x minus 5 is greater than 1 over x. So according to the given question, we have 1 over x minus 5 minus 1 over x is equal to 1 over 10 or x minus x minus 5 over x into x minus 5 is equal to 1 over 10 or x minus x plus 5 over x square minus 5x is equal to 1 over 10 or 5 into 10 which is 50 is equal to x square minus 5x or we have x square minus 5x minus 50 is equal to 0. Now we will find the factors of this quadratic equation. So this can be written as x square minus 10x plus 5x minus 50 is equal to 0 or x into x minus 10 plus 5 into x minus 10 is equal to 0 or x plus 5 into x minus 10 is equal to 0. Now product of two numbers is equal to 0, this implies x plus 5 is equal to 0 or x minus 10 is equal to 0. This implies x is equal to minus 5 or x is equal to 10. So we have two values of x, either x is equal to minus 5 or x is equal to 10. Now x is our larger number, so when the larger number is equal to minus 5 then the smaller number is equal to minus 5 minus 5 which is equal to minus 10 or when the larger number is equal to 10 then the smaller number is equal to 10 minus 5 which is equal to 5. Hence required numbers are either minus 5 and minus 10 or 10 and 5. So this is the answer for the above question. This completes our session. I hope the solution is clear to you. Bye and have a nice day.