The savings of a man is equal to $20\%$ of his expenditure. If his income increases by $25\%$ and expenditure increases by $18\%$, then his savings will increase by:

Let the initial expenditure be $E=100$.Given that savings ($S$) is $20\%$ of the expenditure:
$$S=20\%\text{ of }100=20$$
We know that $\text{Income (I)}=\text{Expenditure (E)}+\text{Savings (S)}$:
$$I=100+20=120$$
Now, according to the new conditions:Income increases by $25\%$:
$$\text{New Income}=120\times \left(1+\frac{25}{100}\right)=120\times 1.25=150$$
Expenditure increases by $18\%$:
$$\text{New Expenditure}=100\times \left(1+\frac{18}{100}\right)=118$$
Calculate the new savings:
$$\text{New Savings}=\text{New Income}-\text{New Expenditure}$$
$$\text{New Savings}=150-118=32$$
Now, let's find the percentage increase in savings:
$$\text{Increase in Savings}=32-20=12$$
$$\text{Percentage Increase}=\left(\frac{12}{20}\right)\times 100=60\%$$