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Answer :
Let unit place digit be x.
Ten’s place digit y= 9 – x[Sum of both digits: x+y=9]
Original number = x + 10(9 – x)
Condition I: 10x + (9 – x) (Interchanging the digits)
Condition II: New number = original number + 27
\(\Rightarrow\) 10x + (9 – x) = x + 10(9 – x) + 27
\(\Rightarrow\) 10x + 9 – x = x + 90 – 10x + 27 (solving the brackets)
\(\Rightarrow\) 9x + 9 = -9x + 117 (Transposing 9x to LHS and 9 to RHS)
\(\Rightarrow\) 9x + 9x = 117 – 9
\(\Rightarrow\) 18x = 108
\(\Rightarrow\) x = 108 ÷ 18 (Transposing 18 to RHS)
\(\Rightarrow\) x = 6
Hence we have,
Unit place digit = 6
Tens place digit = 9 – 6 = 3
Thus, the required number = 6 + 3 × 10 = 6 + 30 = 36