Question

The unit digit of a two digit number is one less than the ten digit number. If the number is increase by 8 and then divided by the unit of the digits, the results is 8. Find the number.

Answer 1

The tens digit is 3; the units digit is 3-1 = 2; and the number itself is 32.

Lets simplify the problem,

Let assume  the "tens" digit be x

Then the "units" difference =  (x-1), according to the condition.

Hence, the number itself is N = 10x + (x-1).

Then the number N+8 is 10x + (x-1) + 8 = 10x + x + 7 = 11x + 7.

From the last statement of the problem, we have this equation

$N+8 = 8*(x+y),or11x + 7 = 8*(x+(x-1)).$

Simplify and find "x"

$11x + 7 = 8*(2x-1)11x + 7 = 16x - 87 + 8 = 16x - 11x15 = 5xx = 15/5 = 3$.

Thus the tens digit is 3; the units digit is 3-1 = 2; and the number itself is 32.

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