Mathematics
The sum of the digits of a two digit number is 9 and the product of the digits is 20. If the unit digit is greater than the tens digit. The number is
45
54
none of these
Quadratic Equations
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Answer
54
Reason
Let tens digit be x and units digit be y.
Given,
x + y = 9
xy = 20
From x + y = 9, we have y = 9 - x
Substituting in xy = 20, we get,
⇒ x(9 - x) = 20
⇒ 9x - x2 = 20
⇒ 9x - x2 - 20 = 0
⇒ x2 - 9x + 20 = 0
⇒ x2 - 4x - 5x + 20 = 0
⇒ x(x - 4) - 5(x - 4) = 0
⇒ (x - 4)(x - 5) = 0
⇒ (x - 4) = 0 or (x - 5) = 0
⇒ x = 4 or x = 5
When x = 4, y = 9 - 4 = 5
When x = 5, y = 9 - 5 = 4
The problem states "the unit digit is greater than the tens digit", so we need y > x.
∴ x = 4 and y = 5
∴ The number is 45
Hence, option 1 is the correct option.
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