 Hello and welcome to the session. Let's work out the following problem It says the sum of the digits of two-digit number is 15 the number obtained by Enterchanging the digits exceed the given number by 9 find the number Let's now move on to the solution. We have to find a two-digit number. So let the digit at 10th place Vx and the digit units place Vy So now the number formed is the given number is 10 x plus y as we know that any two-digit number can be written as 10 into the digit at 10th place plus the digit at units place So the given number is 10 x plus y now We are given that the sum of the two digits is 15. So according to question x plus y is Equal to 15 since we are given that the sum of the digits is 15 This is one of the equation Now we are given that the number obtained by interchanging the digits exceeds the given number by 9 now the number obtained by interchanging digits will be Plus x since we are interchanging the digits the digit at units place will come at 10th place and the digit at 10th place will go at units place So they change their position and we are given that the number obtained by interchanging the digits exceeds the given number by 9 that is if we add 9 to the given number it will be equal to The number obtained by interchanging the digits so again we have 10 x plus y plus 9 is Equal to 10 y plus x since the number obtained by interchanging the digits is 9 more than the given number So from this we have 10 x plus y minus 10 y Minus x is equal to minus 9 So this implies 9 x minus 9 y is equal to minus 9 so this implies taking 9 common we have x minus y is equal to Minus 1 so let's name this as 2 now we'll solve equation 1 and 2 for x and y we add equation 1 and 2 Equation 1 is x plus y is equal to 15 equation 2 is x minus y is equal to minus 1 Now adding to equations x plus x is 2x plus y gets cancelled with minus y 14 minus 1 is 15 minus 1 is 14 So this implies x is 14 by 2 that is 7 now put x is equal to 7 in any one of the two equations So we'll put x is equal to 7 in equation 1 so we have 7 plus y is equal to 15 So this implies y is equal to 15 minus 7 so this implies y is equal to 8 Now we know that the given number is 10 x plus y now x is 7 y is 8 so the number is 10 into 7 is 70 plus 8 so the number is 78 Hence the answer is 78 So this completes the question and the session bye for now take care. Have a good day