Answer:

[tex]let \: the \: digit \: in \: 10th \: place = x \\ the \: digit \: in \: unit \: place \: = y \\ the \: two \: digit \: number = 10x + y \: \\ given \: the \: difference \: of \: digits \\ x - y = 3.......(1) \\ the \: digits \: are \: interchanged \: and \: resulting \: number \: is \: added \: to \: the \: original \\ (10x + y) + (10y + x) = 121 \\ 11x + 11y = 121 \\ x + y = 11.........(2) \\ solving \: (1) \: and \: (2) \: using \: ellimination \: method \: here \\ x - y = 3 \\ x + y = 11 \\ adding \: together \\ 2x = 14 \\ x = \frac{14}{2} = 7 \\ substituting \: x = 7 \: in \: equation \: (1) \\ 7 - y = 3 \\ y = 7 - 3 = 4 \\ the \: original \: number = 10x + y = 10 \times 7 + 4 = 74[/tex]

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