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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.
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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