In a four digit number, the units place digit is one

Solution

Let’s assume the four digit number is ‘dcba‘. In a four-digit number, the unit's place digit is one more than the hundreds place digit. a = c+1    Eq.(i) The tens place digit is one less than the thousand place digit. b = d-1    Eq.(ii) The unit's place digit is two less than the tens place digit. a = b-2    Eq.(iii) The sum of the digits of the number is 20. d+c+b+a = 20    Eq.(iv) Put Eq.(i) and Eq.(ii) in Eq.(iv). d+c+d-1+c+1 = 20 2d+2c = 20 d+c = 10    Eq.(v) Put Eq.(v) in Eq.(iv). 10+b+a = 20 b+a = 20-10 b+a = 10    Eq.(vi) Put the value of ‘a’ from Eq.(iii) into Eq.(vi). b+b-2 = 10 2b = 10+2 2b = 12 b = 6 Put the value of ‘b’ in Eq.(vi). 6+a = 10 a = 10-6 a = 4 Put the value of ‘a’ in Eq.(i). 4 = c+1 c = 4-1 c = 3 Put the value of ‘b’ in Eq.(ii). 6 = d-1 d = 6+1 d = 7 So here we got the values of ‘a ‘, ‘b‘, ‘c‘ and ‘d‘ and there is only two prime digit number in the number.