Mathematics
A two digit number contains the bigger at ten's place. The product of the digits is 27 and the difference between two digits is 6 . Find the number.
Quadratic Equations
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Answer
Let ten's digit be x and one's digit be y.
According to question,
⇒ xy = 27 ……..(i)
⇒ x - y = 6
⇒ x = 6 + y …….(ii)
Substituting value of x from (ii) in (i) we get,
⇒ (6 + y)y = 27
⇒ y2 + 6y = 27
⇒ y2 + 6y - 27 = 0
⇒ y2 + 9y - 3y - 27 = 0
⇒ y(y + 9) - 3(y + 9) = 0
⇒ (y - 3)(y + 9) = 0
⇒ y - 3 = 0 or y + 9 = 0
⇒ y = 3 or y = - 9.
Since digits cannot be negative,
∴ y ≠ -9
x = 6 + y = 6 + 3 = 9
Number = 10(x) + y = 10(9) + 3 = 93.
Hence, number = 93.
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