Question

The sum of the digits of a two digits 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 digits be x and y, and the number be 10x + y.

Then, x + y = 9 ------ (1)

Also, 9*(10x + y) = 2 * (10y + x)

This gives, 90x + 9y = 20y + 2x

Or 88x = 11y or

y = 8x ---- (2)

Substituting the value of y in eqn. 1, we get

x + 8x = 9 or 9x = 9.

Thus, x = 1 and y = 8*1 = 8.

Thus, the number is 10*1 + 8 = 18.