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.
Answers
Damon
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 :)
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 :)
poorvi
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
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