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Question
A two digit number is such that the product of its digit is 8. When 18 is subtracted from the number, the digits interchange its place. Find the numbers.
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Solution
Let this two digit number be xy. Which means x=10x (as it comes in tens digit).
Then as per the question,
xy = 8, ....... (i)
l0x + y - 18 = 10y + x
⇒ 9x-9y-18=0
⇒ x - y - 2 = 0 ....... (ii)
Putting x = `8/"y"` from (i) in (ii) , we get ,
`8/"y" - "y" - 2 = 0`
⇒ y2 + 2y - 8 = 0
⇒ (y-2)(y+4 ) =O
⇒ y = 2, hence from (i), x=4.
Hence the number is 42
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