A person spends $60\%$ of his income. His income increased by $30\%$ and he increased his expenditure by $20\%$. His percent savings will then be increased by:

Let the initial Income = $100$ Expenditure = $60\%$ of $100=60$ Savings = $100-60=40$ New Income after $30\%$ increase:
$$100\times \left(1+\frac{30}{100}\right)=130$$
New Expenditure after $20\%$ increase:
$$60\times \left(1+\frac{20}{100}\right)=72$$
New Savings:
$$130-72=58$$
Increase in savings = $58-40=18$ Percentage increase in savings:
$$\left(\frac{18}{40}\right)\times 100=45\%$$