Question

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 ______.

Options

• 45

• 54

• None of these

Answer 1

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.

Explanation:

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