Question

A no has two digits.The ones-fourth of tens digit.The diffrence between the number and the new number obtained by reversing its digit is 54.Find the original number.

Answer 1

$let \: the \: 10 \: digit \: = x \: \\ unit \: digit \: = 4 \: \\ number \: = 10 \times x \: + 4x \: = 14x \\ after \: reversing \: \\ unit \: digit = x \: \\ tens \: digit \: = 40x \\ number \: = \geqslant 40x + x \: = 41x \\ \\ atq \\ 14x - 41x \: = 54x \\ - 27x \: = 54 \\ x \: = - 54 \div 27 = - 2 \\ \\ so \: the \: original \: no \: = - 2 \times 4x \: - 2 \\ \\ ans \: is \: - 10$