-step explanation:Given :-The SUM of the digits of a two digit number is 10. if 36 is subtracted from the number the digits interchange their places. To FIND :-Find the number ?Solution :-Let the digit at tens place of a two digit number be XThe place value of X = 10×X = 10XLet the digit at ones place of the two digit number be YThe place value of Y = 1×Y = YThen the Original two digit number = 10X+YIf the digits interchanged their places then the new number = 10Y+XGiven thatThe sum of the digits of a two digit number = 10=>X+Y = 10 ---------(1)ANDIF 36 is subtracted from the number the digits interchange their places. => (10X+Y)-36 = 10Y+X=> (10X+Y)-(10Y+X) = 36=> 10X+Y-10Y-X = 36=> 9X-9Y = 36=> 9(X-Y) = 36=> X-Y = 36/9=> X-Y = 4 -------------(2)On adding (1)&(2) thenX+Y = 10X-Y = 4(+)_______2X+0 = 14________=> 2X = 14=> X = 14/2=> X = 7On Substituting the value of X in (1) then=> 7+Y = 10=> Y = 10-7=> Y = 3Therefore, the digits are 7 and 3The number = 73Answer:-The required number for the given problem is 73Check:-The original number = 73The sum of the digits = 7+3 = 10If 36 is subtracted from 73 then=> 73-36=> 37=> Digits are interchanged Verified the given relations in the given problem.