Question

I go to a bank with a cheque written x rs and y paise.the teller by mistake gives paise column as rs and rs column as paise.i spend 5 paise out of the money recd and while checking iam surprised to have double the amount written in the check.though i found the ans by trial and error metod how to find using algebrical method
pls reply

Answer 1

Let x and y be positive integers.

Amount on the cheque A = Rs x  and y paise. = 100 x + y  paise
         as paise are less than 100,     1<=  y <= 99
Actually given amount B = Rs y and x paise. = 100 y + x paise
            1 <= x <= 99

Amount Remaining after 5 paise are spent : B - 5 =   100 y + x - 5 paise
             B - 5 = 2 A
      100 y + x - 5 = 2 (100 x + y)
         98 y - 5 = 199 x

=>  98 y = 199 x + 5
         98  y =  196 x + (3 x + 5 )
             98 (y - 2x) = 3 x + 5

Since  x and y are integers,    y-2x = integer  and is > 0  as RHS is positive.
         3 x + 5 is a multiple of 98.
   => x = (98-5)/3 = 31    one solution.
  => x = (2*98-5)/3 ≠ integer
 =>  x = (3*98-5)/3 ≠ integer
   => x = (4*98-5)/3  > 100  so not a solution.

Hence, x = Rs  31    and  y - 2x = 1  =>  y = 63 paise.