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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.
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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