Question

Find Birth Date and Month
By multiplying my birth date by 31 and month by 12, I got a total of 494. Can you tell me birth date and month?

Answer 1

Suppose A is the birth date and B is the month So we can write as,  

31A+ 12B = 494 ---- (1)31A = 494 - 12B ---- (2)
Now we know that there are 12 month in a year so we check the values of B = 1,2,3......
Since both value must be a positive integer, so the value of B for which A comes as positive integer will satisfy equation (2) and will be our solution.
Case 1: Put  B = 1, than A = 15.54 (Not an integer )           Case 2: Put B = 2, than A = 15.16 (Not an integer )
Case 3: Put B = 3, than A = 14.77 (Not an integer )

Case 4: Put B = 4, than A = 14.38 (Not an integer )

Case 5: Put B = 5, than A = 14 (It is  a pure  integer value)

Put these values in equation 1

31(14) + 12(5) = 494

Value satisfies. So the ans is 14 May.

Answer 2

date = d.  month = m.    we have that  31 * d + 12 * m = 494

RHS is even,  so d is even. Let d = 2n.     31 n + 6m = 247
d and m are integers.  we have   m <= 12
So  n >= (247 - 6 * 12)/31         or,    n >= 6

so now   m = (247 - 31 n)/6

let n = 6,  d = 12,   m = non integer
    n = 7  ,  d =  14,  m = 5

So answer = 14 May.