Question

the sum of digits of a three digit number is 12 and the digit are in ap if the digit are reversed then the number is dimnished by 396 find the number

Answer 1

Let the digits be   a, b, c

Let the common difference be d

Let the numbers be: b - d, b, b + d

b - d + b + b + d = 12

= 3b = 12

=  b      =4

Now, 100c + 10b + a + 396 = 100a + 10b + c

100(b+d) + (b - d) + 396 = 100(b - d) + (b + d)

100(4+d) + (4- d) + 396 = 100(4 - d) + (4 + d)

400 + 100d + 4 - d + 396 = 400 - 100d + 4 + d

198d = -396

d = -2

a = 4- (-2) and c = 4 + (-2)

a = 6  ,  b =4 , and c = 2

Hence the original number is: 642

##check 642-246=396