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Question
A two digit positive number is such that the product of its digits is 6. If 9 is added to the number, the digits interchange their places. Find the number.
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Solution
Let the unit's digit be x then tens digit will be `(6)/x`, then two digit number is `(60)/x + x.`
From question,
`(60)/x + x + 9 = 10x + (6)/x`
60 + x2 + 9x = 10x2 + 6
9x2 - 9x - 54 = 0
x2 - x - 6 = 0
x2 - 3x + 2x - 6 = 0
x (x - 3) + 2 (x - 3) = 0
(x - 3) (x +2) = 0
⇒ x = -2 or 3
As x can't be-ve
So, required two digit number
= `(60)/(3) + 3`
= 23.
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