The price of Petrol increased by $25\%$. In order that expenses on petrol should not increase, one must reduce travel by

Let the initial price of petrol be $100$ and initial consumption be $100$. Initial expenditure = $100\times 100=10000$.New price = $125$. Let the new consumption be $C$.Since expenditure must remain unchanged:
$$125\times C=10000$$
$$C=\frac{10000}{125}=80$$
Reduction in travel/consumption:
$$\text{Reduction}=100-80=20\%$$
Alternative shortcut formula:
$$\text{Percentage reduction}=\left(\frac{R}{100+R}\right)\times 100=\left(\frac{25}{125}\right)\times 100=\frac{1}{5}\times 100=20\%$$