Question

The sum of the digits of a 2-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

Answer 1

Let the number be 10x + y.

Given, x + y = 9  ...(i)

According to the question,

9(10x + y) = 2(10y + x)

∴ 90x + 9y = 20y + 2x

∴ 88x − 11y = 0

∴ 8x − y = 0  ...(ii)

On adding Eqs. (i) and (ii), we get

9x = 9

∴ x = 1

On substituting x = 1 in Eq. (i), we get

1 + y = 9

∴ y = 8

The number is 10x + y = 10 × 1 + 8 = 18

Therefore, x = 1 and y = 8 are the required digits and the number is 18.