A number N consists of two digits. The digit in the tens place is 3 times the digit in the units place. The digits are reversed and the resulting number is denoted by R. If \(N\times R=3627\), then what is the product of the digits of the number N?
27
Let the units digit be \(u\), so the tens digit is \(3u\), giving \(N=31u\) and \(R=13u\). Then \(N\times R=403u^2=3627 \Rightarrow u^2=9 \Rightarrow u=3\). So \(N=93\), with digits 9 and 3. Product of digits \(=9\times3=27\).
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