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Question
A two digits number is such that the product of the digits is 12. When 36 is added to the number, the digits inter change their places determine the number.
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Solution
Let the tens digit be x
Then, the units digit = 12/x
`therefore " Number" =10x+12/x`
And, number obtained by interchanging the Digits `= 10xx12/x+x=120/x+x`
`rArr10x+12/x+36=120/x+x`
`rArr9x+(12-120)/x+36=0`
⇒ 9x2 - 108 + 36x = 0
⇒ 9(x2 + 4x - 12) = 0
⇒ x2 + 6x - 2x - 12 = 0
⇒ x(x + 6) - 2(x + 6) = 0
⇒ (x - 2)(x + 6) = 0
∴ x = 2 or x = -6
But, a digit can never be negative, x = 2
Hence, the digit `=10x+12/x=10(2)+12/2=20+6=26`
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