Aman spends 50% of his income. If income increases by 20% and expenses increases by 10%, his saving will increases by:

Let the income of the person be 2S; if he spends 50% of it, then he is saving 2S - S = S.

If his income increases by 20%, then the income becomes $$2S\ +\ \dfrac{20}{100}\left(2S\right)\ =\ \dfrac{12}{5}S$$

Initially, his expenses were S, and if they increase by 10%, the expenses become $$S\ +\ \dfrac{10}{100}\left(S\right)\ =\ \dfrac{11}{10}S$$

So, his savings in the second case  = $$\dfrac{12}{5}S\ -\ \dfrac{11}{10}S\ =\ \dfrac{\left(24\ -\ 11\right)}{10}S\ =\ \dfrac{13}{10}S$$

The savings increased by a percentage of $$\dfrac{\left(\ \dfrac{13}{10}S\ -\ S\right)}{S}\times\ 100\ =\ \dfrac{3}{10}\ \times\ 100\ =\ 30\%$$

Hence, the correct answer is option B.