Question

The unit digit of two digit number is one less than the tens digit. if the number is increased by 8 and then divided by the sum of the digits the result is 8. find the number

Answer 1

Let the "tens" digit be t.

Then the "units" difit is (t-1), according to the condition.

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

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

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

N+8 = 8*(t+u),

or

11t + 7 = 8*(t+(t-1)).

Simplify and find t

11t + 7 = 8*(2t-1)

11t + 7 = 16t - 8

7 + 8 = 16t - 11t

15 = 5t

t = 15/5 = 3.

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

Hence, the number is 32.