The bar graph given below displays the percentage distribution of a company's total expenditure across various expense categories for the year 2013.



If the expenditure on advertisement is $\text{₹}2.55\text{ crores}$, then the difference between the expenditure on transport and taxes is:

From the given bar chart, the percentages of total expenditure for different sectors are:
* Advertisement = $15\%$
* Transport = $10\%$
* Taxes = $7.5\%$

We are given that:

$$15\%\text{ of total expenditure}=\text{₹}2.55\text{ crores}$$

Let's find the difference in percentage between Transport and Taxes:

$$\text{Difference}=10\%-7.5\%=2.5\%$$

Now, we can use a unitary method to find the value of $2.5\%$:

$$\text{Value of }2.5\%=\frac{2.55\text{ crores}}{15}\times 2.5$$

$$\text{Value of }2.5\%=\frac{2.55}{6}\text{ crores}=0.425\text{ crores}$$

Converting crores into lakhs ($1\text{ crore}=100\text{ lakhs}$):

$$0.425\times 100\text{ lakhs}=42.5\text{ lakhs}$$

Hence, the difference between the expenditure on transport and taxes is $\text{₹}42.5\text{ lakhs}$.