Question
A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is:
Answer: Option B
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Let the ten's and unit digit be x and \(\frac{8}{x}\) respectively.
Then, \(\left(10x+\frac{8}{x}\right)+18 = 10\times\frac{8}{x}+x\)
\(\Rightarrow\) 10x2 + 8 + 18x = 80 + x2
\(\Rightarrow\) 9x2 + 18x - 72 = 0
\(\Rightarrow\) x2 + 2x - 8 = 0
\(\Rightarrow\) (x + 4)(x - 2) = 0
\(\Rightarrow\) x = 2.
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