The price of coal being increased by $20\%$, a family reduces its consumption of coal by $20\%$. By what percent will the family's expenses for coal increase or decrease?

Let the initial price of coal be $\text{Rs. }100$ and the initial consumption be $100\text{units}$.
$$\text{Initial Expenses}=100\times 100=\text{Rs. }10,000$$

* New price after $20\%$ increase = $100\times 1.20=120$
* New consumption after $20\%$ decrease = $100\times 0.80=80$

$$\text{New Expenses}=120\times 80=\text{Rs. }9,600$$

$$\text{Percentage Change in Expenses}=\frac{9,600-10,000}{10,000}\times 100\%=-\frac{400}{10,000}\times 100\%=-4\%$$

Alternatively, using the successive percentage formula $x+y+\frac{xy}{100}$:

$$\text{Net Change}=20-20+\frac{20\times (-20)}{100}=-4\%$$

A negative result implies a $4\%$ decrease.