Question

A number consists of two digits whose sum is 9. If 27 is subtracted from the number, its digits are reversed. Find the number.

Answer 1

Let the units digit be x . 
\[ \because\text{ Sum of two digits }= 9\]
\[ \therefore\text{ Tens digit }= (9 - x)\]
\[ \therefore\text{ Original number }= 10 \times (9 - x) + x\]
 Reversed number = 10x + (9 - x)
According to the question, 
\[10 \times (9 - x) + x - 27 = 10x + (9 - x)\]
\[\text{ or }90 - 10x + x - 27 = 10x + 9 - x\]
\[\text{ or }9x + 9x = 90 - 27 - 9\]
or 18x = 54
\[\text{ or }x = \frac{54}{18} = 3\]
\[ \therefore\text{ The number }= 10 \times (9 - 3) + 3 = 63\]