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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

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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.