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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.
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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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