Question

two two digit numbers are written one after another to give a four digit number such that the larger two digit number is written first. now if the difference of the four digit number and the sum of two two digit numbers is 5742 then find the two digit number.

Answer 1

$$\begin{gathered} \mathrm{Dear}\mathrm{Student}, \\ \mathrm{Let}\mathrm{the}\mathrm{digit}\mathrm{is}\mathrm{xymn},\mathrm{with}\mathrm{xy}\mathrm{larger}\mathrm{digit}. \\ \mathrm{Now} \\ 1000\mathrm{x}+100\mathrm{y}+10\mathrm{m}+\mathrm{n}-\left[10\mathrm{x}+\mathrm{y}+10\mathrm{m}+\mathrm{n}\right]=5742....\left(1\right) \\ 990\mathrm{x}+99\mathrm{y}+0\mathrm{m}+0\mathrm{n}=5000+700+40+2 \\ 99\left[10\mathrm{x}+\mathrm{y}\right]=5742 \\ 99\mathrm{xy}=5742 \\ \mathrm{xy}=58 \\ \mathrm{So}\mathrm{we}\mathrm{can}\mathrm{find}\mathrm{largest}\mathrm{number}\mathrm{only}. \\ \mathrm{Regards} \end{gathered}$$