Question

In a four-digit number, the sum of the digits in the units place and the tens place is equal to the sum of the digits in the hundreds and the thousands places. the sum of the digits in the tens and hundreds place is three times the sum of the other two digits. if the sum of the digits of the number is more than 20, then the digits in the units place can be

Answer 1

let four digit number be 1000a + 100b + 10c + d
and x be one digit number

In a four-digit number, the sum of the digits in the units place and the tens place is equal to the sum of the digits in the hundreds and the thousands places

so,c + d = a + b...........(1)

the sum of the digits in the tens and hundreds place is three times the sum of the other two digits

so,b + c = 3(a + d)
c = 3a + 3d - b...........(2)

substitute (2) in (1)
3a + 3d - b + d = a + b
3a - a + 4d = b + b
2a + 4d = 2b
b = a + 2d..........(3)

the sum of the digits of the number is more than 20

so, a + b + c + d >20 ( to eliminate > symbol I introduce a variable x)
a + b + c + d = 20 + x..........(4)

substitute (1) in (4)
a + b + a + b = 20 + x
2a + 2b = 20 + x

substitute (3) in (4)
2a + 2(a + 2d) = 20 + x
2a + 2a + 4d = 20 + x
4a + 4d = 20 + x
4d = 20 + x - 4a
d = (20 + x - 4a)/4

digit in unit place is d = (20 + x - 4a)/4