Suppose we call the digits ABCD. We have
D = 2*C
B = D - 5
A = C + B
Expressing these in terms of C, we have
B = 2*C - 5
A = C + 2*C - 5 = 3*C - 5
We know every digit must be in the range 0 to 9, so we have
9 ≥ 2C - 5 ≥ 0
14 ≥ 2C ≥ 5 (add 5)
7 ≥ C ≥ 2.5 (divide by 2)
9 ≥ 3C - 5 ≥ 0
14 ≥ 3C ≥ 5 (add 5)
4 2/3 ≥ C ≥ 1 2/3 (divide by 3)
In order to satisfy both these conditions, we must have C = {3, 4}. This gives rise to two possible solutions. For C=3, we have D=6, B=1, A=4. For C=4, we have D=8, B=3, A=7. The possible solutions are
4136
7348
D = 2*C
B = D - 5
A = C + B
Expressing these in terms of C, we have
B = 2*C - 5
A = C + 2*C - 5 = 3*C - 5
We know every digit must be in the range 0 to 9, so we have
9 ≥ 2C - 5 ≥ 0
14 ≥ 2C ≥ 5 (add 5)
7 ≥ C ≥ 2.5 (divide by 2)
9 ≥ 3C - 5 ≥ 0
14 ≥ 3C ≥ 5 (add 5)
4 2/3 ≥ C ≥ 1 2/3 (divide by 3)
In order to satisfy both these conditions, we must have C = {3, 4}. This gives rise to two possible solutions. For C=3, we have D=6, B=1, A=4. For C=4, we have D=8, B=3, A=7. The possible solutions are
4136
7348