The sum of the two digits of a number is 10. If the number is subtracted from the number obtained by reversing its digits, the result is 54. Find the number?
Any two digit number can be written as \((10P + Q)\), where \(P\) is the digit in the tens place and \(Q\) is the digit in the units place.
\(P + Q = 10\) ----- (1)
\((10Q + P) - (10P + Q) = 54\)
\(9(Q - P) = 54\)
\((Q - P) = 6\) ----- (2)
Solve (1) and (2) \(P = 2\) and \(Q = 8\)
The required number is \(= 28 \)