Description for Correct answer:
Let the first number be x.

Thereforer, second number = \( \frac{15}{18}x \)

According to question,

\( x + \frac{5}{18} = 506 \)

\( \frac{23}{18}x = 506 \)

\( x = 396 \)

Therefore, sercond number = 110

Required difference = \( \frac{4}{9} \times 396 - \frac{2}{11} \times 110 \)

\( = 176 - 20 = 156 \)