Question

In a three digit number, the hundreds digit is twice the units digit. If the digits are reversed, the new number is 396 less than the original number. Find the number.

Answer 1

a b c = 100 a + 10 b + c

a = 2 c

reversed c b a = 100 c + 10 b + a
100 a + 10 b + c - 100 c - 10 b - a = 396

99 a - 99 c = 396
but a = 2 c so
198 c - 99 c = 396
99 c = 396
c = 4
then a = 8
so
8 b 4
what if b is 1 ?
is 814 - 418 = 396 ????
yes
what if b is 3?
is 834 - 438 = 396 ???
yes
In fact I suspect the middle digit can be about any :)

Answer 2

a b c = 100 a + 10 b + c

a = 2 c

reversed c b a = 100 c + 10 b + a
100 a + 10 b + c - 100 c - 10 b - a = 396

99 a - 99 c = 396
but a = 2 c so
198 c - 99 c = 396
99 c = 396
c = 4
then a = 8
b might be 1 or 3 however the difference is same