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Question
A two digit number is such that the product of the digit is 12. When 36 is added to the number, the digits interchange their places. Find the numbers.
Solution
Let this two digit number be xy. Which means x=10x (as it comes in tens digit).
Then as per the question,
xy = 12, ....... (i)
10x + y + 36 = 10y + x
⇒ 9x - 9y + 36 = 0
⇒ x - y + 4 = 0 ....... (ii)
Putting x = `12/"y"` from (i) in (ii) , we get,
`12/"y" - "y" + 4 = 0`
⇒ y2 - 4y - 12 = 0
⇒ y2 - 6y + 2y - 12 = 0
⇒ y ( y - 6 ) +2 (y-6) = 0
⇒ (y - 6)(y + 2) = 0
⇒ y = 6, hence from (i), x=2.
Hence the number is 26
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