A two-digit number is such that four times the sum of its digits is equal to the number formed by reversing its digits. If the difference between the digits is 3, find the original number.
63
Let the tens digit be x and units digit be y. The condition gives \(4(x+y) = 10y+x\) (the reversed number).
Simplifying: \(4x+4y=10y+x \Rightarrow 3x=6y \Rightarrow x=2y\).
With \(x-y=3\) and \(x=2y\): \(2y-y=3 \Rightarrow y=3,\ x=6\).
Original number: \(10x+y = 63\).
Hence, the original number is 63.
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