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Question
A two digit number is such that the product of its digit is 14. When 45 is added to the number, then the digit interchange their places. Find the number.
Solution
Let the ten's digit be x, then unit's digit = `(14/x)`
Then, the number is `(10x +14/x)`
Where 45 is added to the number, the digits get interchanged.
∴ `10x + (14)/x + 45 = 10 xx (14)/x + x`
⇒ x2 + 5x - 14 = 0
⇒ (x + 7) (x + 2) = 0
⇒ x = 2
and x = -7 (inadmissible)
Hence, the number is `(10x + 14/x)`
= `(10 xx 2 + 14/2)`
= 27.
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