The-unit-digit-of-a-two-degit-number-is-1-less-than-the-tens-degit-if-the-number-is-increased-by-8-and-then-divided-by-the-sum-of-the-digits-the-result-is-8-Find-the-number-

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Question Number 168073 by pete last updated on 02/Apr/22

The unit digit of a two degit number is 1 less than the tens degit. if the number is increased by 8 and then divided by the sum of the digits, the result is 8. Find the number.

$$\mathrm{The}\:\mathrm{unit}\:\mathrm{digit}\:\mathrm{of}\:\mathrm{a}\:\mathrm{two}\:\mathrm{degit}\:\mathrm{number}\:\mathrm{is}\:\mathrm{1}\:\mathrm{less} \\ $$$$\mathrm{than}\:\mathrm{the}\:\mathrm{tens}\:\mathrm{degit}.\:\mathrm{if}\:\mathrm{the}\:\mathrm{number}\:\mathrm{is}\:\mathrm{increased} \\ $$$$\mathrm{by}\:\mathrm{8}\:\mathrm{and}\:\mathrm{then}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{digits},\:\mathrm{the}\:\mathrm{result}\:\mathrm{is}\:\mathrm{8}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{number}. \\ $$

Answered by som(math1967) last updated on 02/Apr/22

10′s digit x unit digit=x−1 number=10x+x−1=11x−1 11x−1+8=8(2x−1) 7+8=5x x=3 unit digit=3−1=2 number is 32 ans (32+8)÷(3+2)=8

$$\mathrm{10}'{s}\:{digit}\:{x} \\ $$$${unit}\:{digit}={x}−\mathrm{1} \\ $$$${number}=\mathrm{10}{x}+{x}−\mathrm{1}=\mathrm{11}{x}−\mathrm{1} \\ $$$$\mathrm{11}{x}−\mathrm{1}+\mathrm{8}=\mathrm{8}\left(\mathrm{2}{x}−\mathrm{1}\right) \\ $$$$\mathrm{7}+\mathrm{8}=\mathrm{5}{x} \\ $$$${x}=\mathrm{3} \\ $$$${unit}\:{digit}=\mathrm{3}−\mathrm{1}=\mathrm{2} \\ $$$${number}\:{is}\:\mathrm{32}\:{ans} \\ $$$$\left(\mathrm{32}+\mathrm{8}\right)\boldsymbol{\div}\left(\mathrm{3}+\mathrm{2}\right)=\mathrm{8} \\ $$

Commented by som(math1967) last updated on 02/Apr/22