Unknown number

[kate]

Find the unknown two-digital number ab for which we know that 8ab = 126 + ab8, where a and b are digits.

[Guest]

the question is really good one
here is the answer

we know,
126
+ab8
------
8ab

sum of last digits of 126 and ab8 is 6+8 which is equal to 14 that is 4 with 1 carry
therefore we come to the inference that b=4

so the addition now becomes,

1(carry)
126
+a48
------
8a4


adding the middle digits 1+2+4 is equal to 7
therefore,a=7

so the answer ab is 74

we can verify also,

126
+748
-------
874






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