Question

The difference between the digits of a two-digit number is 2 and the product of digits is 24. If tens digit is bigger, the number is ______.

Options

• 24

• 26

• 46

• 64

Answer 1

The difference between the digits of a two-digit number is 2 and the product of digits is 24. If tens digit is bigger, the number is 64.

Explanation:

Let the unit digit be x then tens digit = x + 2

Since the tens digit is given to be greater than unit digit

Also, x(x + 2) = 24

`\implies` x² + 2x – 24 = 0

`\implies` x² + 6x – 4x – 24 = 0

`\implies` x(x + 6) – 4(x + 6) = 0

`\implies` (x – 4)(x + 6) = 0

Either x – 4 = 0 or x + 6 = 0

`\implies` x = 4 or x = – 6

Since unit digit cannot be negative

∴ x ≥ 0

∴ x = 4

Thus, the number becomes

= 10(x + 2) + x

= 10(4 + 2) + 4

= 60 + 4

= 64