correct answer is: a) 49 & 77

Explanation

Two numbers ratio are 7 : 11
Let, one number is = 7x
Another number is = 11x
According to the question,
\left(7x+7\right) ∶ \left(11x+7\right)\ =\ 2\ ∶\ 3
\rightarrow\ \frac{7x+7}{11x+7}\ =\ \frac{2}{3}
\rightarrow\ 2\left(11x+7\right)\ =\ 3\left(7x\ +\ 7\right) _{[cross multiply]}
\rightarrow\ 22x\ +\ 14=21x+21
\rightarrow\ 22x-21x\ =\ 21-14 _{[interchange]}
\rightarrow\ x=7
\therefore One number is = 7x or \left(7\times7\right)
\rightarrow\ 49
And, another number is = 11x or \left(11\times7\right)
\rightarrow\ 77
Ans: One number is 49,
Another number is 77.