Question

The tens digit of a certain two-digit number exceeds the units digit by 4 and is 1 less than twice the units digit. Find the digit number.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{digit}\mathrm{at}\mathrm{unit}\text{'}\mathrm{s}\mathrm{place}=x \\ \mathrm{so},\mathrm{the}\mathrm{digit}\mathrm{at}\mathrm{ten}\text{'}\mathrm{s}\mathrm{place}=x+4 \\ \mathrm{Now},\mathrm{original}\mathrm{number}=10\left(x+4\right)+x=11x+40 \\ \mathrm{Now},\mathrm{according}\mathrm{to}\mathrm{condition}, \\ \mathrm{digit}\mathrm{at}\mathrm{ten}\text{'}\mathrm{s}\mathrm{place}=2\left(\mathrm{digit}\mathrm{at}\mathrm{unit}\text{'}\mathrm{s}\mathrm{place}\right)-1 \\ \Rightarrow x+4=2x-1 \\ \Rightarrow x-2x=-1-4 \\ \Rightarrow -x=-5 \\ \Rightarrow x=5 \\ \mathrm{So},\mathrm{original}\mathrm{number}=11x+40=11\times 5+40=55+40=95 \end{gathered}$$