A number 4

A number is made up of two digits. The sum of the digits is 11. if the digits are interchanged, the original number is increase by 9. Find the original number

Correct answer:

x =  56

Step-by-step explanation:

$$\begin{gathered} a+b=11 \\ 10\cdot a+b+9=10\cdot b+a \\ a+b=11 \\ 9a-9b=-9 \\ a=5 \\ b=6 \\ x=10\cdot a+b=10\cdot 5+6=56 \end{gathered}$$

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