Find all 8-digit numbers 273A49B5 which are divisible by 11 as well as 25.

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Solution

The given number is 273A49B5 .

A number is divisible by 11 if the difference between the sum of the digits at even places and the sum of the digits at odd places is divisible by 11.

2 − 7 + 3 − A + 4 − 9 + B − 5 = B − A − 12

B − A − 12 is divisible by 11, if B − A = 1

The number is divisible by 25, if A = 1, B = 2 or A = 6, B = 7

Hence, the numbers are 27314925 and 27364975.

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