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Let the tenth place be x and the units place be y the no.=10x+y x+y=11 -(1) if the digits are reversed unit=x and tenth place =y the no.=10y+x (10x+y) +27=10y+x 10y+x - 10x-y=27 9y-9x=27 9(y-x)=27 y-x=3(27divided by 3) -x +y=3 -(2)

x + y = 11 -x+y = 3 --------------- 0+2y=14 2y=14 y=7 y=7 in equation (1)

let the unit digit be x since the sum of the digits is 11 , the tenth digit is 11 - x therefore , the number is = (11-x)*10+x = 110 - 10x + x = 110 - 9x if 27 is added , then the number is reversed , 110 - 9x + 27= 9x + 11 - 9x - 9x = 11 - 110 - 27 - 18x = - 126 x = 126/18 = 7 therefore , the original number is = 110 - 9x = 110 - (9*7) = 110 - 63 = 47