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Verified answer
Given :
To find :
Unit digit of 2-digit number.
Let :
Solution :
According to question,
Condition 1)
The unit digit of 2digit number is 6 more than the digits at tens place
➝ x = 6 + y
➝ y = x - 6 equation 1
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Condition 2)
Product of tens and unit digit is 12 less than the 2-digit number
➝ (x)(y) = [ 10y + x ] - 12 equation 2
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Put value of y(= x - 6 ) from equation 1 into equation 2,
➝ (x)( x-6) = [ 10(x-6) + x ] - 12
➝ x² - 6x = 10x - 60 + x - 12
➝ x² - 6x = 11x - 72
➝ x² - 6x - 11x + 72 = 0
➝ x² - 17x + 72 = 0
[ Note - Splitting middle term. ]
➝ x² - (8+9)x + 72 = 0
➝ x² - 8x - 9x + 72 = 0
➝ x(x-8) - 9(x-8) = 0
➝ (x-8)(x-9) = 0
Either. (x-8) = 0 or (x-9) = 0
Either ( x = 8 ) or. ( x = 9 )
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Therefore, unit place for given 2 digit number can be either 8 or 9
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ANSWER :
Possible Unit digit = Either 8 or 9
So,
So,
Now,
According to statement,
So,