Question

If 18 is added to a two-digit number, its digits are reversed. If the product of the digits of the number is 24, the number is ______.

Options

• 46

• 64

• 56

• 48

Answer 1

If 18 is added to a two-digit number, its digits are reversed. If the product of the digits of the number is 24, the number is 46.

Explanation:

Let the unit and tens digits are x and y

∴ Required two digit number = 10y + x

According to the given conditions,

xy = 24   ...(1)

Also, 10y + x + 18 = 10x + y

`\implies` 9y – 9x + 18 = 0

`\implies` 9(y – x + 2) = 0

`\implies` y – x = – 2

`\implies` x – y = + 2   ...(2)

From (1); y = `24/x` putting in equation (2);

`x - 24/x = 2`

`\implies (x^2 - 24)/x = 2`

`\implies` x² – 24 = 2x

`\implies` x² – 2x – 24 = 0

`\implies` x² – 6x + 4x – 24 = 0

`\implies` x(x – 6) + 4(x – 6) = 0

`\implies` (x – 6)(x + 4) = 0

Either x – 6 = 0 or x + 4 = 0

`\implies` x = 6 or x = – 4

Since x ≥ 0

∴ x = 6

∴ From (1); 6y = 24

`\implies` y = 4

Thus, the required number = 10y + x

= 10 × 4 + 6

= 40 + 6

= 46