In a four digit number, the units place digit is one more than the hundreds place digit and the tens place digit is one less than the thousand place digit and the units place digit is two less than the tens place digit. The sum of the digits of the number is 20. How many prime number digits are there in the number.

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.