correct answer is: b) 15 & 27

Explanation

Two numbers ratio are 5 : 9
Let, one number is = 5x
Another number is = 9x
According to the question,
\left(5x-3\right)∶ \left(9x-3\right)\ =\ 1\ ∶\ 2
\rightarrow\ \frac{5x-3}{9x-3}\ =\ \frac{1}{2}
\rightarrow2\left(5x-3\right)=1\left(9x-3\right) _{[cross multiply]}
\rightarrow\ 10x-6=9x-3
\rightarrow\ 10x-9x\ =-\ 3\ +\ 6 _{[interchange]}
\rightarrow\ x=3
\therefore One number is = 5x or \left(5\times3\right)
\rightarrow\ 15
And, another number is = 9x or \left(9\times3\right)
\rightarrow\ 27
Ans: One number is 15,
Another number is 27.