 Hello and welcome to the session. The given question says, the sum of two numbers is eight. Determine the numbers of the sum of their reciprocals is eight divided by fifteen. Let's start with the solution. Here we are given that the sum of two natural numbers is equal to eight. So let the numbers be, and if one number is x then other is eight minus x. Now we are further given that the numbers if reciprocate them then their sum is equal to eight divided by fifteen. So according to the question one divided by x plus one divided by eight minus x is equal to eight divided by fifteen. Or we further have x into eight minus x. In the numerator we have eight minus x plus x is equal to eight divided by fifteen. Or we have eight divided by x into eight minus x is equal to eight divided by fifteen. Or in cross multiplying we have x into eight minus x is equal to fifteen. Which further implies that x square minus eight x plus fifteen is equal to zero. Now as splitting the middle term it can further be written as x square minus three plus five into x plus fifteen is equal to zero. Or we have x square minus three x minus five x plus fifteen is equal to zero. Now taking x common from the first two terms and minus five common from the last two terms we have x into x minus three minus five into x minus three is equal to zero. Or we have x minus three into x minus five is equal to zero. Now we know that if the product of two numbers is equal to zero then either a is equal to zero or we have b is equal to zero. So this implies that x minus three is equal to zero or x minus five is equal to zero. So this implies x is equal to three or five. So this is the first number. So the other number will be eight minus three that is five or eight minus five that is three. Hence the answer is the two natural numbers are three or five. So this completes the session. Bye and take care.